Discussion
What is the angle between the hour hand and the minute hand of a clock when the clock shows 10 hours 10 minutes ?
Answer: C
The angle is 245°, the reflex angle.
The angle between the hands at \(H\) hours \(M\) minutes is \(|30H - 5.5M|\).
\[ \begin{aligned} |30 \times 10 - 5.5 \times 10| &= |300 - 55| \\ &= 245^\circ \end{aligned} \]
The smaller angle between the hands is \(360^\circ - 245^\circ = 115^\circ\), which is not among the options, so the keyed answer is the reflex angle of 245°. 240° (or 120°) is what you get by leaving the hour hand fixed on the 10, forgetting that it moves 5° past it in 10 minutes.
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