What is the smaller angle between the hands of a clock at 4:40 a.m.?

The correct answer is Option (4) → 100°

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 4:40: \(4\times30^\circ+40\times0.5^\circ=120^\circ+20^\circ=140^\circ\)

• Minute hand at 40 minutes: \(40\times6^\circ=240^\circ\)

• Angle between them \(=240^\circ-140^\circ=100^\circ\), less than 180°, so it is the smaller angle