7.5 degrees.
The minute hand is pointing directly at the '3'. The hour hand is 1/4 of the way between the '3' and '4'. Since there are 12 numbers the angle between each number is 30 degrees. So the angle between the hands are 30 degrees * 1/4 = 7.5 degrees.
Google Riddles - The Big Hand and the Small Hand
Riddle:
What is the angle between the big hand and the small hand when the time is 3:15?
(The 'Google Riddles' are interview questions those who wish to get hired were asked).