What is the angle between the minute and hour hands of the clock at 8:40 PM?

At 8:00 PM, the hour hand is at 240 degrees from vertical (12 o'clock).

In 40 minutes, the hour hand will move 40*(0.5) = 20 degrees ( since the hour hand moves at 0.5 degrees per minute). The hour hand made an angle (240+20) = 260 degrees from the vertical.

In 40 minutes, the minute hand will move 40*(6) = 240 degrees from the vertical. ( since the minute hand moves at 6 degrees per minute)

Hence, the angle between the hand is (260-240) = 20 degrees.

The correct option is C.