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To determine the angle between the hour hand and the minute hand at 6:10PM.
We know the one round of the clock is 360 degrees. So the hour hand covers this in 12 hours =12*60 minutes = 720 minutes. So every minute the hour hand covers 360 /720 = 1/2 degree. So at 6:10 hours = 6*60+10 minutes = 370 minutes, the hour hand describes an angle of 370*1/2 = 185 degree from 12 o'clock position.
We assume the angles in degrees are measured from the 12 O'clock position.
The minute hand covers one round in 60 minutes. So every mnute it covers 360/60 = 6 degree. Therefore the minute hand at 10 minutes past 6 o'clock should describe an angle 10*6 = 60 degree from the postion of the number 12 (or when it was at 6 o'clock postion).
Therefore the angle between the hour hand and minute hand is the difference of the angle they described from the 12 O'clock position. So the angle between the clock hands at 6:10PM = 185 deg - 60 deg = 125 degree.
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