What is the angle between the two hands of a clock at 10:25 p.m.?

The correct answer is Option (3) → 162.5°

Measure both hands clockwise from 12: the minute hand at 6° a minute, the hour hand at 30° an hour plus 0.5° a minute.

• Hour hand at 10:25: \(10\times30^\circ+25\times0.5^\circ=300^\circ+12.5^\circ=312.5^\circ\)

• Minute hand at 25 minutes: \(25\times6^\circ=150^\circ\)

• Angle between them \(=312.5^\circ-150^\circ=162.5^\circ\), which is less than 180°, so it is the angle between the hands