Assuming they just want an estimate based on looking at a clock at any given time, this would be my methodology: 1) A circle is 360 degrees 2) A clock has 60 minutes 3) 1 minute = 6 degrees 4) Look at the position of the big hand and little hand, estimate their degrees based on the minutes past 12, and find the difference. e.g. At 3:30: the little hand is halfway between 3 and 4 (17.5 minutes past 12), so 17.5*6 = 105 degrees from 12. The big hand is at 30 minutes, 30*6=180 degrees from 12. So the angle between the big hand and little hand is 180-105=75 degrees.