What is the smaller angle between the hands of a clock at 8:24 a.m.?

The correct answer is Option (3) → 108°

Measure both hands clockwise from 12. The minute hand turns 6° a minute; the hour hand turns 30° an hour and 0.5° a minute, so it has moved on past the hour mark as the minutes go by.

• Hour hand at 8:24: \(8\times30^\circ+24\times0.5^\circ=240^\circ+12^\circ=252^\circ\)

• Minute hand at 24 minutes: \(24\times6^\circ=144^\circ\)

• Angle between them \(=252^\circ-144^\circ=108^\circ\), which is less than 180°, so it is the smaller angle