Clock Angle at 3:15 PM

At 3:15 PM, the minute hand is at $90^\circ$ (pointing directly at 3). The hour hand moves at $0.5^\circ$ per minute. In 15 minutes, the hour hand moves $15 \times 0.5^\circ = 7.5^\circ$ past 3. Thus, the angle between the two hands is $7.5^\circ$, which equals 7 degrees and 30 minutes.