A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute.

Equation for the angle of the hour hand

ΘH = (60H+M)/2

 

Equation for the degrees on the minute hand

ΘM= 6M

M= Minute and H = Hour

Angle between Hour and minute handle

ΘH - ΘM