At what angle are the hour hand and the minute hand of a clock inclined at 15 min past 5?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(67\frac{1}{2}\)°
Measure each hand’s position clockwise from the 12. The minute hand moves 6° a minute. The hour hand moves 30° an hour, and also half a degree every minute, so at 5:15 it has gone a quarter of the way from 5 towards 6.
Minute hand at 15 minutes: \(15\times6=90^\circ\) (on the 3)
Hour hand at 5:15: \(5\times30+15\times\frac{1}{2}=150+7.5=157.5^\circ\)
Angle between them: \(157.5-90=67.5^\circ=67\frac{1}{2}^\circ\)
Shortcut: The angle at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\).
\(\displaystyle \left|30\times5-\frac{11}{2}\times15\right|=|150-82.5|=67.5^\circ\)