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

The angle between the hour hand and the minute hand of a clock at H hours and M minutes is given by the formula: Angle = |30H − 5.5M| degrees, where H is the hour (in 12-hour format) and M is the number of minutes. If this value exceeds 180 degrees, the actual angle taken is 360 degrees minus this value, since the angle between the hands can be measured on either side.

1. Identify the given time: H = 8 hours, M = 35 minutes.

2. Compute 30H = 30 × 8 = 240°.

3. Compute 5.5M = 5.5 × 35 = 192.5°.

4. Apply the formula: Angle = |240 − 192.5| = |47.5| = 47.5°.

Cross-check using individual hand positions: the minute hand is at 6 × 35 = 210° from 12, and the hour hand is at 30 × 8 + 0.5 × 35 = 240 + 17.5 = 257.5° from 12. The difference is |257.5 − 210| = 47.5°, which confirms the result.

Since 47.5° is less than 180°, it is already the smaller angle between the two hands, so the angle between the hour hand and the minute hand at 8:35 is 47.5°.