For a standard analog clock, what is the angle between the hour hand and the…

On a standard 12-hour analog clock, the minute hand sweeps 6° every minute (360°/60), while the hour hand sweeps 0.5° every minute (30° per hour, since it covers 360° in 12 hours). So the hour hand keeps drifting continuously between hour marks, not staying fixed. The angle between the two hands at H hours and M minutes equals the absolute difference between their positions measured from the 12 o'clock mark, taking the smaller of the angle and its 360° complement if it exceeds 180°.

For 3:35, H = 3 and M = 35. Locate each hand's position from the 12 o'clock mark:

1. Minute hand position = 6° × 35 = 210°.

2. Hour hand position = 30° × 3 + 0.5° × 35 = 90° + 17.5° = 107.5°.

3. Angle between the hands = |210° − 107.5°| = 102.5°.

4. Since 102.5° is less than 180°, it is already the smaller angle between the hands.

Cross-check with the direct formula Angle = |30H − 5.5M|: |30 × 3 − 5.5 × 35| = |90 − 192.5| = 102.5°, matching the step-by-step result.

Hence, the angle between the hour and minute hands at 3:35 am is 102.5°.