An accurate clock shows 8 O’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 O’clock in the afternoon ?

Solve by noting the hour hand’s angular rate and the elapsed hours. The hour hand makes one full revolution (360°) in 12 hours, so it turns 30° per hour (360°/12) [1]. From 8:00 AM to 2:00 PM is a span of 6 hours. Multiplying the rate by the elapsed time gives the rotation: 30°/hour × 6 hours = 180°. Thus the hour hand rotates through 180° between 8 AM and 2 PM, so option 4 is correct. The calculation directly follows the standard clock-angle relation and the stated hour difference [1].

Sources

1. [1] https://en.wikipedia.org/wiki/Clock_angle_problem