Let's solve
Challenge 1 and
Challenge 2 step by step.
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✔ Understanding the Task
Each challenge has two parts:
1.
Draw angles of given sizes (e.g., 35°, 70°, etc.) — this is a practical drawing task.
2.
Calculate missing angles in diagrams where angles are on a straight line or form a full rotation.
We'll focus on the
calculating missing angles part since that’s the mathematical problem-solving component.
> 🔴 Remember: Angles on a
straight line add up to
180°, and angles around a
point add up to
360°.
All diagrams show angles on a straight line (a straight angle), so we use:
>
Missing angle = 180° – given angle
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## 🟦
Challenge 1: Calculate Missing Angles
a) Given: 167°
- The angle shown is
167°, and it's on a straight line.
- So, missing angle = 180° – 167° =
13°
✔ Answer: 13°
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b) Given: 57°
- Missing angle = 180° – 57° =
123°
✔ Answer: 123°
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c) Given: 61°
- Missing angle = 180° – 61° =
119°
✔ Answer: 119°
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d) Given: 122°
- Missing angle = 180° – 122° =
58°
✔ Answer: 58°
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e) Given: 47°
- Missing angle = 180° – 47° =
133°
✔ Answer: 133°
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f) Given: 18°
- Missing angle = 180° – 18° =
162°
✔ Answer: 162°
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## 🟨
Challenge 2: Calculate Missing Angles
a) Given: 131°
- Missing angle = 180° – 131° =
49°
✔ Answer: 49°
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b) Given: 149°
- Missing angle = 180° – 149° =
31°
✔ Answer: 31°
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c) Given: 38°
- Missing angle = 180° – 38° =
142°
✔ Answer: 142°
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d) Given: 118°
- Missing angle = 180° – 118° =
62°
✔ Answer: 62°
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e) Given: 120°
- Missing angle = 180° – 120° =
60°
✔ Answer: 60°
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f) Given: 166°
- Missing angle = 180° – 166° =
14°
✔ Answer: 14°
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##
✔ Final Answers Summary
Challenge 1
| Part | Missing Angle |
|------|----------------|
| a) | 13° |
| b) | 123° |
| c) | 119° |
| d) | 58° |
| e) | 133° |
| f) | 162° |
Challenge 2
| Part | Missing Angle |
|------|----------------|
| a) | 49° |
| b) | 31° |
| c) | 142° |
| d) | 62° |
| e) | 60° |
| f) | 14° |
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## 📝 Explanation
All these problems involve
angles on a straight line, which always sum to
180°. Since only one angle is given in each diagram, the missing angle is simply:
>
180° − given angle
This is a fundamental concept in geometry — useful for solving many real-world problems involving lines and directions.
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💡 Tip: When drawing angles (Part 1), use a protractor carefully. For example, to draw a 70° angle, place the protractor at the vertex, align the baseline with one arm, then mark 70° and draw the second arm.
Let me know if you'd like help sketching any of these!
Parent Tip: Review the logic above to help your child master the concept of 5th grade angle worksheet.
