Angles on the Clock with Examples and Quiz | Preparation

Angles on the Clock

A clock not only tells us the time but also helps us learn geometry. The angle formed between the hour hand and the minute hand can be calculated using simple steps.

Step 1: Understanding Movement of Hands

Fact 1: The minute hand moves 360° in 60 minutes → 6° per minute.

Fact 2: The hour hand moves 360° in 12 hours → 30° per hour, or 0.5° per minute.

Step 2: Formula for Angle

Formula: Angle = |(30 × Hours − (11/2 × Minutes))| If the result is more than 180°, subtract it from 360° to get the smaller angle.

Step 3: Solved Examples

• At 3:00 → Angle = 90°
• At 6:00 → Angle = 180°
• At 9:15 → Angle = |270 − 82.5| = 187.5° → Smaller angle = 172.5°

Step 4: Practice Quiz

Choose the correct option:

1. At 3:00, the angle is: (a) 180° (b) 90° (c) 120°
2. At 6:00, the smaller angle is: (a) 180° (b) 90° (c) 120°
3. At 9:00, the smaller angle is: (a) 270° (b) 90° (c) 60°
4. At 12:30, the smaller angle is: (a) 180° (b) 165° (c) 90°
5. At 4:00, the angle between the hands is: (a) 150° (b) 120° (c) 60°
6. At 2:00, the angle is: (a) 60° (b) 120° (c) 90°
7. At 10:00, the angle is: (a) 120° (b) 150° (c) 60°
8. At 1:30, the angle is: (a) 135° (b) 150° (c) 165°
9. At 7:00, the smaller angle is: (a) 150° (b) 120° (c) 90°
10. At 11:00, the angle is: (a) 30° (b) 60° (c) 90°

Show Answers

1. (b) 90°
2. (a) 180°
3. (b) 90°
4. (b) 165°
5. (b) 120°
6. (a) 60°
7. (b) 150°
8. (a) 135°
9. (a) 150°
10. (a) 30°