Discussion
At 40 past 4 in the evening, the smaller angle between the hour and minute hands of a clock is :
Answer: D
The smaller angle is 100°.
The angle between the hands at H hours M minutes is \(|30H - 5.5M|\):
\[ \begin{aligned} |30 \times 4 - 5.5 \times 40| &= |120 - 220| \\ &= 100^\circ \end{aligned} \]
At 4:40 the minute hand points at 8 (240°) and the hour hand has moved two-thirds of the way from 4 to 5 (140°), so they are 100° apart. Forgetting the hour hand's movement gives 120°, which is not offered.
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