What is the angle of a clock's hands when the clock shows 3:15?

360 degrees in a full circle. 90 degrees per quarter (that breaks up every 3 hours segment).

So that's 30 degrees per hour. Each hour can be broken up into 4 parts (one for every 15 minutes), 30/4 = 7.5 degrees.

The minute hand would point to 3, and the hour hand would be 1/4 of the way to 4. It is a quarter of the way to 4, because only 15 minutes (which is 1/4 of 60 mintes) have passed.