Chapter 52: Measuring and Solving Angles
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Measuring and Solving Angles in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Angle meaning (The mean is found by adding all values and dividing by the number of values.)
- Acute angles (Acute angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Right angles (Right angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Obtuse angles (Obtuse angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Straight angles (Straight angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Reflex angles (Reflex angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
52.1 Angle meaning
The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find the mean of [4, 6, 8, 10].
- Add the values to get 28.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 7
Worked Example 2
Problem: Find the mean of [5, 7, 7, 9, 12].
- Add the values to get 40.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 8
Worked Example 3
Problem: Find the mean of [3, 5, 8, 8, 11].
- Add the values to get 35.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 7
Worked Example 4
Problem: Find the mean of [10, 12, 14, 16].
- Add the values to get 52.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 13
Worked Example 5
Problem: Find the mean of [2, 4, 6, 8, 10].
- Add the values to get 30.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 6
Worked Example 6
Problem: Find the mean of [1, 5, 5, 6, 13].
- Add the values to get 30.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 6
Worked Example 7
Problem: Find the mean of [20, 25, 25, 30].
- Add the values to get 100.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 25
Worked Example 8
Problem: Find the mean of [7, 8, 9, 10, 11].
- Add the values to get 45.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 9
Worked Example 9
Problem: Find the mean of [3, 3, 4, 5, 9].
- Add the values to get 24.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 4.8
Worked Example 10
Problem: Find the mean of [12, 15, 18, 21].
- Add the values to get 66.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 16.5
Practice Exercise
Create one new Grade 6 problem about Angle meaning. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.2 Acute angles
Acute angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Acute angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.3 Right angles
Right angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Right angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.4 Obtuse angles
Obtuse angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Obtuse angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.5 Straight angles
Straight angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Straight angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.6 Reflex angles
Reflex angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Reflex angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.7 Using a protractor
Using a protractor is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Using a protractor. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.8 Estimating angles
Estimating angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Estimating angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.9 Adjacent angles
Adjacent angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Adjacent angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.10 Angles on a straight line
Angles on a straight line is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Two adjacent angles form a straight line. One is 35°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 35.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 145°
Worked Example 2
Problem: Two adjacent angles form a straight line. One is 48°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 48.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 132°
Worked Example 3
Problem: Two adjacent angles form a straight line. One is 67°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 67.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 113°
Worked Example 4
Problem: Two adjacent angles form a straight line. One is 72°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 72.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 108°
Worked Example 5
Problem: Two adjacent angles form a straight line. One is 110°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 110.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 70°
Worked Example 6
Problem: Two adjacent angles form a straight line. One is 25°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 25.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 155°
Worked Example 7
Problem: Two adjacent angles form a straight line. One is 58°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 58.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 122°
Worked Example 8
Problem: Two adjacent angles form a straight line. One is 83°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 83.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 97°
Worked Example 9
Problem: Two adjacent angles form a straight line. One is 95°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 95.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 85°
Worked Example 10
Problem: Two adjacent angles form a straight line. One is 120°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 120.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 60°
Practice Exercise
Create one new Grade 6 problem about Angles on a straight line. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.11 Angles around a point
Angles around a point is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Angles around a point. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.12 Finding unknown angles
Finding unknown angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Two adjacent angles form a straight line. One is 35°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 35.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 145°
Worked Example 2
Problem: Two adjacent angles form a straight line. One is 48°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 48.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 132°
Worked Example 3
Problem: Two adjacent angles form a straight line. One is 67°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 67.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 113°
Worked Example 4
Problem: Two adjacent angles form a straight line. One is 72°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 72.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 108°
Worked Example 5
Problem: Two adjacent angles form a straight line. One is 110°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 110.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 70°
Worked Example 6
Problem: Two adjacent angles form a straight line. One is 25°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 25.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 155°
Worked Example 7
Problem: Two adjacent angles form a straight line. One is 58°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 58.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 122°
Worked Example 8
Problem: Two adjacent angles form a straight line. One is 83°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 83.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 97°
Worked Example 9
Problem: Two adjacent angles form a straight line. One is 95°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 95.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 85°
Worked Example 10
Problem: Two adjacent angles form a straight line. One is 120°. Find the other.
- Angles on a straight line total 180°.
- Subtract: 180 - 120.
Very beginner explanation: A straight angle measures 180°, so adjacent parts must add to 180°.
Answer: 60°
Practice Exercise
Create one new Grade 6 problem about Finding unknown angles. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
52.13 Angle word problems
Angle word problems is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify an angle measuring 35°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 2
Problem: Classify an angle measuring 48°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 3
Problem: Classify an angle measuring 67°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 4
Problem: Classify an angle measuring 72°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 5
Problem: Classify an angle measuring 110°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 6
Problem: Classify an angle measuring 25°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 7
Problem: Classify an angle measuring 58°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 8
Problem: Classify an angle measuring 83°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Acute
Worked Example 9
Problem: Classify an angle measuring 95°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Worked Example 10
Problem: Classify an angle measuring 120°.
- Compare the measure with 90° and 180°.
Very beginner explanation: Angle names depend on their measure.
Answer: Obtuse
Practice Exercise
Create one new Grade 6 problem about Angle word problems. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
30 Review Questions and Answers
Q1. What is important to understand about Angle meaning?
Answer: The mean is found by adding all values and dividing by the number of values.
Q2. What is important to understand about Acute angles?
Answer: Acute angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q3. What is important to understand about Right angles?
Answer: Right angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q4. What is important to understand about Obtuse angles?
Answer: Obtuse angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q5. What is important to understand about Straight angles?
Answer: Straight angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q6. What is important to understand about Reflex angles?
Answer: Reflex angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q7. What is important to understand about Using a protractor?
Answer: Using a protractor is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q8. What is important to understand about Estimating angles?
Answer: Estimating angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q9. What is important to understand about Adjacent angles?
Answer: Adjacent angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q10. What is important to understand about Angles on a straight line?
Answer: Angles on a straight line is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q11. What is important to understand about Angles around a point?
Answer: Angles around a point is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q12. What is important to understand about Finding unknown angles?
Answer: Finding unknown angles is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q13. What is important to understand about Angle word problems?
Answer: Angle word problems is a Grade 6 mathematics idea in Measuring and Solving Angles. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q23. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q24. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q25. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q26. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q27. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q28. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q29. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q30. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.