The angle between the hour hand and the minute hand of a clock when the time is 4:25 PM will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(17\frac{1}{2}^\circ\)
Measure both hands clockwise from 12. The minute hand goes round 360° in 60 minutes, that is, 6° a minute; the hour hand goes 30° in an hour, that is, 0.5° a minute, so at 4:25 it has moved on past the 4.
Minute hand: \(25\times6^\circ=150^\circ\) (on the 5)
Hour hand: \(4\times30^\circ+25\times0.5^\circ=120^\circ+12.5^\circ=132.5^\circ\)
Angle between them \(=150^\circ-132.5^\circ=17.5^\circ=17\frac{1}{2}^\circ\)
Tip: The angle at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\); here \(\left|120-137.5\right|=17.5^\circ\).