What angle do the two hands of a clock make at half past eleven?

The correct answer is Option (2) → 165°

At half past the hour the hour hand is halfway between two numbers. Measure both hands clockwise from 12: minute hand 6° a minute, hour hand 30° an hour plus 0.5° a minute.

• Hour hand at 11:30: \(11\times30^\circ+30\times0.5^\circ=330^\circ+15^\circ=345^\circ\)

• Minute hand at 30 minutes: \(30\times6^\circ=180^\circ\)

• Angle between the hands \(=345^\circ-180^\circ=165^\circ\)

• 150° would be right only if the hour hand stayed on the 11; it has moved 15° towards the 12