The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

Angle traced by hour hand in 17/2 hrs = 360/12 x 17/2 = 225 degree.

Angle traced by min. hand in 30 min. = 360/60 x 30 = 180 degree.

Required angle = (255 - 180) degree= 75 degree.