Grade 6 math worksheet featuring eight problems where students calculate unknown angles formed by lines and rays.

Let's solve each of the problems on the worksheet step by step. The goal is to identify the unknown angles using basic geometry principles, especially:

- Angles on a straight line add up to 180°
- A right angle is 90°
- Angles around a point add up to 360°
- Vertically opposite angles are equal

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1. ∠XOZ = ?

We have:
- Line XY is horizontal.
- OZ is vertical and forms a 90° angle with OY (right angle symbol).
- So, ∠YOZ = 90°
- Since XOY is a straight line, ∠XOY = 180°
- Therefore, ∠XOZ = 180° – ∠YOZ = 180° – 90° = 90°

✔ Answer: 90°

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2. ∠ROQ = ?

Given:
- Line PQ is straight → ∠POQ = 180°
- ∠POR = 105°
- We need ∠ROQ

So:
∠ROQ = 180° – ∠POR = 180° – 105° = 75°

✔ Answer: 75°

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3. ∠ACD = ?

Given:
- Line AB is straight → ∠ACB = 180°
- ∠DCB = 60°
- So, ∠ACD = 180° – 60° = 120°

✔ Answer: 120°

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4. ∠ACD = ?

Given:
- Line AB is straight → ∠ACB = 180°
- ∠DCB = 30°
- So, ∠ACD = 180° – 30° = 150°

✔ Answer: 150°

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5. ∠XQP = ?

Given:
- Line XY is straight → ∠XQY = 180°
- ∠PQY = 135°
- So, ∠XQP = 180° – 135° = 45°

✔ Answer: 45°

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6. ∠PTS = ?

Given:
- Line PQ is straight → ∠PTQ = 180°
- ∠PTQ = 120° (angle between PT and TQ)
- So, ∠PTS = 180° – 120° = 60°

✔ Answer: 60°

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7. ∠XYB = ?

Given:
- Line AB is straight → ∠AYB = 180°
- ∠AYX = 15°
- So, ∠XYB = 180° – 15° = 165°

✔ Answer: 165°

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8. ∠SOQ = ?

Given:
- Line PQ is straight → ∠POQ = 180°
- ∠POS = 100°
- So, ∠SOQ = 180° – 100° = 80°

✔ Answer: 80°

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✔ Final Answers:

1. ∠XOZ = 90°
2. ∠ROQ = 75°
3. ∠ACD = 120°
4. ∠ACD = 150°
5. ∠XQP = 45°
6. ∠PTS = 60°
7. ∠XYB = 165°
8. ∠SOQ = 80°

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🔍 Explanation Summary:

All these problems involve angles on a straight line, which always sum to 180°. The key idea is:

> If two angles form a straight line, their sum is 180°.

So, if one angle is given, subtract it from 180° to find the other.

Also, in problem 1, we used the fact that a right angle is 90°, and since X–O–Y is a straight line, and Z is perpendicular to Y, then ∠XOZ must also be 90°.

Let me know if you'd like this explained visually or with diagrams!