At what angle the hands of a clock are inclined at 20 min past 6?

The correct answer is Option (3) → 70°

Both hands are measured in degrees from the 12. The minute hand moves 6° a minute (360° in 60 minutes), and the hour hand moves 30° an hour, that is, 0.5° a minute, so at 20 past 6 it has moved on from the 6.

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

• Hour hand: \(6\times30^{\circ}+20\times0.5^{\circ}=180^{\circ}+10^{\circ}=190^{\circ}\) from the 12

• Angle between the hands \(=190^{\circ}-120^{\circ}=70^{\circ}\)

Tip: The angle at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\) degrees, a result worth memorising: at 6:20 it gives \(|180-110|=70^{\circ}\) at once.