Find the measure of the smaller angle formed by the hands of a clock at the following time. \( 1: 15 \) The angle is \( \square^{\circ} \square^{\prime} \). (Simplify your answers.)

To find the angle between the hour and minute hands of the clock at 1:15, we can use the following formula: 1. **Minute Hand**: The minute hand moves at \(6\) degrees per minute. At 15 minutes, it will be: \[ 15 \times 6 = 90^\circ \] 2. **Hour Hand**: The hour hand moves at \(30\) degrees per hour (since 360 degrees/12 hours = 30 degrees per hour) plus an additional \(0.5\) degrees for each minute (30 degrees/60 minutes = 0.5 degrees per minute). At 1:15, the hour hand will be: \[ 1 \times 30 + 15 \times 0.5 = 30 + 7.5 = 37.5^\circ \] 3. **Calculating the angle between the two hands**: \[ \text{Angle} = |90 - 37.5| = 52.5^\circ \] Thus, the measure of the smaller angle formed by the hands of the clock at 1:15 is \(52.5^\circ\).