What is the angle between the hour hand and the minute hand of a clock at 9:12?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 156°
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. The angle between the hands is the smaller of the two angles they make.
Hour hand at 9:12: \(9\times30^\circ+12\times0.5^\circ=270^\circ+6^\circ=276^\circ\)
Minute hand at 12 minutes: \(12\times6^\circ=72^\circ\)
Difference \(=276^\circ-72^\circ=204^\circ\), which is more than 180°
Angle between the hands \(=360^\circ-204^\circ=156^\circ\)
