Question

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? 

• A. 144$^{\circ}$
• B. 150$^{\circ}$
• C. 168$^{\circ}$
• D. 180$^{\circ}$
• E.

Hint:

For clock problems, calculate how much the hands move per hour and then multiply by the time difference.

Answer 1

The Correct Option is D

To calculate the rotation of the hour hand, we must consider the number of hours passed between 8 o'clock and 2 o'clock. 
The hour hand moves 360° in 12 hours. Therefore, it moves: $$ \frac{360^\circ}{12} = 30^\circ \text{ per hour.} $$ From 8 o'clock to 2 o'clock is a span of 6 hours, so the hour hand will rotate: $$ 6 \times 30^\circ = 180^\circ. $$ Thus, the answer is (d) 180$^{\circ}$. 

Answer 2

Use the fraction of a full circle the hour hand covers, instead of computing a per-hour rate.

1. The hour hand completes one full \( 360^{\circ} \) rotation every 12 hours.
2. From 8 in the morning to 2 in the afternoon is exactly 6 hours, which is \( \frac{6}{12} = \frac{1}{2} \) of the 12-hour cycle.
3. Half of a full rotation is \( \frac{1}{2} \times 360^{\circ} = 180^{\circ} \).

Checking the other options, \( 144^{\circ} \), \( 150^{\circ} \) and \( 168^{\circ} \) would each correspond to less than half of a full rotation, which does not match the exact 6-hour, half-cycle gap between the two times.

Hence, the correct answer is \( 180^{\circ} \).