Identifying Unknown Angles Worksheets | Geometry - Free Printable

I'll solve this worksheet by identifying the unknown angles in each problem. I'll need to use basic geometry principles like the fact that a straight line equals 180° and perpendicular lines form 90° angles.

Let me work through each problem one by one:

Problem 1: ∠xoz
- We have a right angle (90°) between z and y
- x and y form a straight line (180°)
- So ∠xoz = 180° - 90° = 90°

Problem 2: ∠roq
- p, o, q form a straight line (180°)
- The angle between p and r is 105°
- So ∠roq = 180° - 105° = 75°

Problem 3: ∠acd
- a, c, b form a straight line (180°)
- The angle between c and d is 60°
- So ∠acd = 180° - 60° = 120°

Problem 4: ∠acd
- a, c, b form a straight line (180°)
- The angle between c and d is 30°
- So ∠acd = 180° - 30° = 150°

Problem 5: ∠xqp
- x, q, y form a straight line (180°)
- The angle between q and p is 135°
- So ∠xqp = 180° - 135° = 45°

Problem 6: ∠pts
- p, t, q form a straight line (180°)
- The angle between t and s is 120°
- So ∠pts = 180° - 120° = 60°

Problem 7: ∠xyb
- a, y, b form a straight line (180°)
- The angle between x and y is 15°
- So ∠xyb = 180° - 15° = 165°

Problem 8: ∠soq
- p, o, q form a straight line (180°)
- The angle between p and s is 100°
- So ∠soq = 180° - 100° = 80°

The answers are:
1. ∠xoz = 90°
2. ∠roq = 75°
3. ∠acd = 120°
4. ∠acd = 150°
5. ∠xqp = 45°
6. ∠pts = 60°
7. ∠xyb = 165°
8. ∠soq = 80°