The hour hand is $\frac{20}{60}=\frac{1}{3}$ of the way from the 3 o'clock to the 4 o'clock position, so it has moved $\frac{1}{3}\cdot\frac{1}{12}\cdot 360^\circ=10$ degrees past the 3 o'clock position.  The minute hand is in the 4 o'clock position, so it has moved $\frac{1}{12}\cdot 360^\circ=30$ degrees past the 3 o'clock position.  The angle between the hour hand and the minute hand is $30-10=\boxed{20}$ degrees.
At 3:20, what is the degree measure of the acute angle formed by the hour hand and the minute hand on a 12-hour analog clock?
{'answer': '20', 'subject': 'Prealgebra', 'level': 4, 'unique_id': 'test/prealgebra/517.json'}