1. **State the problem:** Find the exact radian measure of the angle between the hour hand and the minute hand of a clock at 7 o'clock. 2. **Formula and rules:** - Each hour on the clock represents an angle of $\frac{2\pi}{12} = \frac{\pi}{6}$ radians. - The minute hand at 0 minutes points at 12, which is 0 radians. - The hour hand at 7 o'clock points at 7 hours. 3. **Calculate the angle:** - Angle of hour hand from 12:00 is $7 \times \frac{\pi}{6} = \frac{7\pi}{6}$ radians. - Angle of minute hand from 12:00 is $0$ radians. 4. **Find the difference:** $$\text{Angle difference} = \left| \frac{7\pi}{6} - 0 \right| = \frac{7\pi}{6}$$ 5. **Adjust to the smaller angle:** - The clock is circular, so the smaller angle between hands is the minimum of the angle difference and $2\pi$ minus the angle difference. - Calculate $2\pi - \frac{7\pi}{6} = \frac{12\pi}{6} - \frac{7\pi}{6} = \frac{5\pi}{6}$. - The smaller angle is $\frac{5\pi}{6}$ radians. **Final answer:** The exact radian measure of the angle between the hour and minute hands at 7 o'clock is $\boxed{\frac{5\pi}{6}}$ radians.