This problem is a simple mathematical calculation. Lets start deriving some equations. Note: Here we are talking about the round clock, which displays 1-12 hours.
Angle of Minute hand at a particular time
A complete round of a clock is equal to 360 degree angle. This is simple, minute hand complete 360 degree in 60 minutes. Or, it takes 60 minutes to complete 360 degree
60 M -> 360 degree 1 M -> 360/60 -> 6 degree Means, minute hands moves 6 degree per minute. For 'M' minutes, it will be 6 * M degree
Angle of Hour hand at a particular time
Hour hand takes 12 hours to complete a round i.e. 360 degree. But, if you notice. When hour hand moves, there will be a movement in minute hand too, due to that hour hand will move to some extent.
For hour hand: 12 Hours -> 360 degree 1 Hour -> 360/12 -> 30 degree For 'H' Hours -> 30 * H degree And, there will be some movement in minute hand too. Continuing above equation: 12 Hours -> 360 degree 12 * 60 Minutes -> 360 degree 1 Minute -> 360 / (12 * 60) -> 1/2 degree In 'M' minuets -> M/2 degree Combining them, Angle of hour : 30 H + M/2
Difference of Angle between Hour and Minute hand
As from above equations:
Angle of Hour hand - Angle of Minute hand => (30 H + M/2) - (6 M) => 30 H - 5.5 M
Angle at time: 6:15
30 H - 5.5 M => 30 * 6 - 5.5 * 15 => 180 - 82.5 => 97.5