Find the angle formed by the hour hand and the minute hand of a clock at 3:25.

The angle between a clock's hour hand and minute hand at H hours and M minutes is found by measuring each hand's position in degrees clockwise from 12 and taking the absolute difference. The minute hand sweeps 6 degrees every minute (360/60). The hour hand sweeps 30 degrees every hour (360/12) but also creeps forward an extra 0.5 degrees every minute (30/60), since it keeps moving between hour marks as minutes pass. So: minute-hand position = 6M, hour-hand position = 30H + 0.5M, and angle = |6M - (30H + 0.5M)| = |5.5M - 30H| (take 360 degrees minus this value if it exceeds 180 degrees, since the angle asked for is the smaller one).

1. Minute hand position at 25 minutes past the hour = 6 x 25 = 150 degrees.

2. Hour hand position at 3:25 = 30 x 3 + 0.5 x 25 = 90 + 12.5 = 102.5 degrees.

3. Angle between the hands = |150 - 102.5| = 47.5 degrees.

4. Since 47.5 degrees is already less than 180 degrees, no further adjustment is needed - it is the angle asked for.

Cross-check with the compact form of the same formula, theta = |60H - 11M| / 2: |60 x 3 - 11 x 25| / 2 = |180 - 275| / 2 = 95 / 2 = 47.5 degrees, confirming the result.

Hence, the angle formed by the hour and minute hands at 3:25 is 47.5 degrees.