How many degrees are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?
The stupid and quick answer would be 0 degree.
But, if we rethink again, it's not the case exactly. When the minute hand points to '15' (quarter), the hour hand has moved little bit. How many? Let's analyze!
To make a full-circle (360 degrees rotation), the hour hand has to pass 12 hours, thus for one hour, it takes 360 degrees/12 = 30 degrees. For a quarter hour = 1/4 * 30 = 7.5 degrees.
So the answer is: 7.5 degrees.