Question

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

Answer 1

Of course the minute hand will be at the 45 minute mark, if we let 12:00 to correspond with 0°, then
the minute hand is at 270°
each hour the hour hand moves 30°, (360/12 = 30)
so at a quarter to six it has moved 180 - (1/4)(3)° = 172.5

so the acute angle between the two hands is 270-172.5 = 97.5°