Question

Find the angle between the hands of a clock when the clock shows 4:30

Answer 1

At 4:30 the minute hand is at 6 and so it makes an angle of 6*30 = 180 deg from 12.

At 4:30 the hour hand is between 4 and 5 and it makes an angle of 4*30+30*30/60 = 120+15 = 135 deg from 12.

So the two hands of the clock make an angle of 180–135 = 45 deg.