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ANSWER: 7.5 degrees.

EXPLANATION: When it is 3:15, the hour hand will be on the 3 while the minute hand will be one quarter of the way from the 3 to the 4 (since a quarter of an hour has passed). There are 360 degrees in a circle and 12 numbers on the clock therefore there are 30 degrees between the 3 and the 4. With the hour hand a quarter of the way between the 3 and 4 and the minute hand exactly on the 3, the two hands are separated by 30/4 = 7.5 degrees.

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