What is the smaller angle between the hands of a clock at 1:20 a.m.?

The correct answer is Option (3) → 80°

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 1:20: \(1\times30^\circ+20\times0.5^\circ=30^\circ+10^\circ=40^\circ\)

• Minute hand at 20 minutes: \(20\times6^\circ=120^\circ\)

• Angle between them \(=120^\circ-40^\circ=80^\circ\), less than 180°, so it is the smaller angle