Clock 2

At 20 minutes past 2, the hour hand has traveled 1/3 of the rotation from the 2 to the three. This corresponds to an angle of $(2+\frac{1}{3})\cdot\frac{\pi}{6}=\frac{7\pi}{18}$ clockwise from 12. The minute hand is pointing at 4, at an angle of $4\cdot\frac{\pi}{6}=\frac{2\pi}{3}$ clockwise from 12. Therefore, the angle between the hands of the clock is $\frac{2\pi}{3}-\frac{7\pi}{18}=\frac{5\pi}{18}$ , or $\boxed{50^\circ}$ .