Discussion
At what angle the hands of a clock are inclined at 15 minutes past 5?
Answer: B
The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \theta = \left| 30(5) - 5.5(15) \right| = \left| 150 - 82.5 \right| \]
\[ = 67.5^{\circ} \]
The minute hand sits on the 3 and the hour hand a quarter of the way past the 5, so the gap is a little under the \( 60^{\circ} \) between the 3 and the 5.
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