Let's solve each problem step by step using the properties of angles at a point or on a straight line.
---
Key Concepts:
1.
Angles on a straight line add up to
180°.
2.
Angles around a point add up to
360°.
3. A
right angle is
90°.
We'll use these rules to find the value of $ x^\circ $ in each case.
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Problem 1:
- Two angles are shown: one is $ 15^\circ $, and the other is $ x^\circ $.
- They form a straight line (since they're adjacent and make a straight path).
- So, their sum is $ 180^\circ $.
$$
x + 15 = 180 \\
x = 180 - 15 = 165^\circ
$$
✔ Answer: $ \angle x^\circ = 165^\circ $
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Problem 2:
- One angle is $ 30^\circ $, the other is $ x^\circ $.
- These two angles lie on a straight line.
$$
x + 30 = 180 \\
x = 180 - 30 = 150^\circ
$$
✔ Answer: $ \angle x^\circ = 150^\circ $
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Problem 3:
- The diagram shows a right angle (marked with a square), and another angle of $ 125^\circ $.
- The three angles together form a full turn around a point: total $ 360^\circ $.
- But note: the right angle is $ 90^\circ $, and there’s a $ 125^\circ $ angle.
- The third angle is $ x^\circ $.
So:
$$
x + 90 + 125 = 360 \\
x + 215 = 360 \\
x = 360 - 215 = 145^\circ
$$
✔ Answer: $ \angle x^\circ = 145^\circ $
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Problem 4:
- There’s a right angle ($ 90^\circ $) and a $ 60^\circ $ angle.
- These two angles are adjacent and together with $ x^\circ $ make up a right angle? Wait — let’s look carefully.
Actually:
- The vertical line and horizontal line form a
right angle ($ 90^\circ $).
- Inside that right angle, there are two parts: one is $ 60^\circ $, and the other is $ x^\circ $.
- So, $ x^\circ $ and $ 60^\circ $ together make $ 90^\circ $.
$$
x + 60 = 90 \\
x = 90 - 60 = 30^\circ
$$
✔ Answer: $ \angle x^\circ = 30^\circ $
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Problem 5:
- Three angles are on a straight line: $ 60^\circ $, $ x^\circ $, and $ 60^\circ $.
- Sum of angles on a straight line = $ 180^\circ $
$$
60 + x + 60 = 180 \\
x + 120 = 180 \\
x = 180 - 120 = 60^\circ
$$
✔ Answer: $ \angle x^\circ = 60^\circ $
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Problem 6:
- Two angles on a straight line: $ 75^\circ $ and $ x^\circ $.
- They form a straight line → sum = $ 180^\circ $
$$
x + 75 = 180 \\
x = 180 - 75 = 105^\circ
$$
✔ Answer: $ \angle x^\circ = 105^\circ $
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✔ Final Answers:
| Problem | $ \angle x^\circ $ |
|--------|---------------------|
| 1 | 165° |
| 2 | 150° |
| 3 | 145° |
| 4 | 30° |
| 5 | 60° |
| 6 | 105° |
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🔍 Summary of Concepts Used:
- Angles on a straight line: $ 180^\circ $
- Angles around a point: $ 360^\circ $
- Right angle: $ 90^\circ $
These problems reinforce understanding of basic angle relationships without needing a protractor. Great practice for Grade 6! 🎯
Parent Tip: Review the logic above to help your child master the concept of 6th grade math worksheet angles.
