What is the smaller angle between the hands of a clock at 12:40 a.m.?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 140°
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. At 12:40 the hour hand has moved on only from the 12 mark.
Hour hand at 12:40: \(0^\circ+40\times0.5^\circ=20^\circ\)
Minute hand at 40 minutes: \(40\times6^\circ=240^\circ\)
Difference \(=240^\circ-20^\circ=220^\circ\), which is more than 180°
Smaller angle \(=360^\circ-220^\circ=140^\circ\)
