Question

When the time is 8:30, the angle between the minute hand and the hour hand of a clock is:

• A.
• B.
• C.
• D.

Hint:

When calculating angles between the hour and minute hands, first find the positions of both hands and then calculate their difference. If the result is greater than 180°, subtract it from 360° to get the smallest angle.

Answer 1

The Correct Option is B

To find the angle between the minute and hour hand at 8:30, we follow these steps: - At 8:00, the hour hand is at the 8th position. The minute hand is at the 12th position. - The angle between each hour on the clock is \( \frac{360^\circ}{12} = 30^\circ \). - So, at 8:00, the hour hand is at \( 8 \times 30^\circ = 240^\circ \) from the 12 o'clock position. - At 8:30, the minute hand is at the 6th position (30 minutes), which is \( 180^\circ \) from the 12 o'clock position. - The angle between the hour and minute hands is the difference between their positions: \( 240^\circ - 180^\circ = 60^\circ \). Therefore, the angle between the two hands is \( 180^\circ - 60^\circ = 105^\circ \). Thus, the correct answer is (B) 105°.