The angle between the minute hand and the hour hand of a clock when the time is 8:30

Angle traced by hour hand in 17/2 hrs =  $\frac{360}{12}\times \frac{17}{2}o$ = 255 

Angle traced by min hand in 30 min =  $\frac{360}{60}\times 30o$ = 180 

Therefore,  Required angle = (255 - 180) =  $75o$