At 3:40 p.m., what is the angle between the hour hand and the minute hand of a clock?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 130°
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, so at 3:40 the hour hand has moved two-thirds of the way from 3 to 4.
Hour hand at 3:40: \(3\times30^\circ+40\times0.5^\circ=90^\circ+20^\circ=110^\circ\)
Minute hand at 40 minutes: \(40\times6^\circ=240^\circ\)
Angle between them \(=240^\circ-110^\circ=130^\circ\), which is less than 180°, so it is the angle between the hands
