At what angle are the hour and minute hands of a clock inclined at 15…

The correct answer is Option (4) → \(67\frac{1}{2}^{\circ}\)

Measure both hands from the 12. The minute hand turns 6° a minute (360° in 60 minutes); the hour hand turns 30° an hour, that is, ½° a minute, so at 5:15 it has moved a quarter of the way from 5 towards 6.

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

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

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

Tip: The angle between the hands at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\); here \(\left|150-82\frac{1}{2}\right|=67\frac{1}{2}^\circ\). If the result is more than 180°, subtract it from 360°.