Question

Find the angle between hour-hand and minute-hand in a clock at quarter to six.

Answer 1

The angle between any two consecutive numbers of a clock is `(360°)/12` = 30°.

If the minute-hand is at 9 and hour-hand is at 5, angle between them is (4 × 30°) = 120°.

But at quarter to six, i.e., at 5.45, the hour-hand has moved 45 minutes towards 6.

In 60 minutes, the hour-hand covers 30°, therefore in 45 minutes, it covers `((45 × 30)/60)^circ` = 22°30'

∴ The angle between the two hands of the clock at quarter to six= 120° – 22°30' = 97°30'.