Find the degree measure of the angle between the hour and minute hands of the clock at 12 hours 15 minutes.

Since the hour hand moves continuously, and not discretely, jumping one division every hour, its position at 12 hours 15 minutes corresponds to an intermediate value between the divisions of 12 hours and 1 hour.

There are 60 minutes in one hour, therefore 15 minutes is 15/60 = 1/4 hour. Therefore, the arrow is 1/4 of the way from division 12 to division 1.

The angle between two hour divisions is 360 ° / 12 = 30 °. Therefore, 1/4 of this angle is 30 ° / 4 = 7.5 °.

The minute hand shows exactly 15 minutes, which corresponds to an angle of 15/60 * 360 ° = (15 * 6) ° = 90 ° relative to the division of 0 minutes, which coincides with the division of 12 hours.

Thus, the angle between the two arrows is 90 ° – 7.5 ° = 82.5 °.

Answer: 82.5 °.