What is the angle between the hands of a clock at 6:12 a.m.?

The correct answer is Option (4) → 114°

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 6:12: \(6\times30^\circ+12\times0.5^\circ=180^\circ+6^\circ=186^\circ\)

• Minute hand at 12 minutes: \(12\times6^\circ=72^\circ\)

• Angle between them \(=186^\circ-72^\circ=114^\circ\), which is less than 180°, so it is the angle between the hands