The reflex angle between the hands of the clock at 9:20 is

The correct answer is Option (2) → 200°

Each minute the minute hand turns \(6^\circ\) and the hour hand \(0.5^\circ\), so each hand’s position can be measured clockwise from 12. The two positions give the smaller angle between the hands, and the reflex angle is the larger one, \(360^\circ\) minus the smaller angle.

• Minute hand at 20 minutes: \(20\times6^\circ=120^\circ\) from 12

• Hour hand at 9:20: \(9\times30^\circ+20\times0.5^\circ=280^\circ\) from 12

• Smaller angle between them: \(280^\circ-120^\circ=160^\circ\)

• Reflex angle: \(360^\circ-160^\circ=200^\circ\)

Tip: 160°, Option (1), is the smaller angle between the hands; a reflex angle is always more than 180°, so the answer is the other side of the clock.