What will be the angle between the hands of the clock at 8:30?

The correct answer is Option (2) → 75°

The minute hand turns \(360^\circ\) in 60 minutes, that is \(6^\circ\) per minute. The hour hand turns \(30^\circ\) in an hour, that is \(0.5^\circ\) per minute. Both are measured from the 12.

• Hour hand at 8:30: \(8\times30^\circ+30\times0.5^\circ=240^\circ+15^\circ=255^\circ\)

• Minute hand at 30 minutes: \(30\times6^\circ=180^\circ\)

• Angle between them \(=255^\circ-180^\circ=75^\circ\)

Shortcut: At H hours M minutes, the angle between the hands is \(\left|30H-\frac{11}{2}M\right|\).

• \(\left|30\times8-\frac{11}{2}\times30\right|=\left|240-165\right|=75^\circ\)

Tip: At 8:30 the hour hand is halfway between the 8 and the 9, not on the 8. Taking it on the 8 gives \(60^\circ\), which is Option (4).