What is the larger angle between the hands of a clock at 3:28 p.m.?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 296°
The two hands make two angles that together form a full turn of 360°. Find the smaller one first, with the minute hand at 6° a minute and the hour hand at 30° an hour plus 0.5° a minute, then subtract it from 360°.
Hour hand at 3:28: \(3\times30^\circ+28\times0.5^\circ=90^\circ+14^\circ=104^\circ\)
Minute hand at 28 minutes: \(28\times6^\circ=168^\circ\)
Smaller angle \(=168^\circ-104^\circ=64^\circ\)
Larger angle \(=360^\circ-64^\circ=296^\circ\)
