What is the smaller angle between the hands of a clock at 11:48 a.m.?

The correct answer is Option (2) → 66°

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 11:48: \(11\times30^\circ+48\times0.5^\circ=330^\circ+24^\circ=354^\circ\)

• Minute hand at 48 minutes: \(48\times6^\circ=288^\circ\)

• Angle between them \(=354^\circ-288^\circ=66^\circ\), less than 180°, so it is the smaller angle

Why the other options are incorrect

• Option (1) 42° — Incorrect. This takes the hour hand still at the 11 mark (330°), forgetting its 24° move in 48 minutes.

• Option (3) 72° — Incorrect. This takes the hour hand already at the 12 mark (360°); at 11:48 it is still 6° short of 12.

• Option (4) 294° — Incorrect. This is the larger angle \(360^\circ-66^\circ\), not the smaller one.