At what angle are the hands of a clock inclined at 15 minutes past 5?

The correct answer is Option (2) → \(67\frac{1}{2}^\circ\)

The minute hand turns \(360^\circ\) in 60 minutes, that is \(6^\circ\) a minute; the hour hand turns \(30^\circ\) in an hour, that is \(\frac{1}{2}^\circ\) a minute. Both positions are measured from 12.

• Hour hand at 5:15: \(\displaystyle 5\times30+15\times\frac{1}{2}=150+7\frac{1}{2}=157\frac{1}{2}^\circ\)

• Minute hand at 15 minutes: \(15\times6=90^\circ\)

• Angle between them \(\displaystyle =157\frac{1}{2}-90=67\frac{1}{2}^\circ\)

Tip: At H hours M minutes the angle between the hands is \(\left|30H-\frac{11}{2}M\right|\) degrees (subtract it from \(360^\circ\) if it is more than \(180^\circ\)). Here \(|150-82.5|=67.5^\circ\).