What is the measure of the smaller of the two angles formed between the hour hand and the minute hand of a clock when it is 5:49 p.m.?
The hour hand moves 360 degrees every 12 hours. At 5:49, its angle is $$(5 + \frac{49}{60}) \times\frac{ 360}{12} = 174.5 degrees$$
The minute hand moves 360 degrees each 60 minutes, so at 15 minutes past the hour it has moved $$\frac{49}{60} \times 360 = 294 degrees.$$
Thus, the difference between the two hands is 294 - 174.5 = 119.5 degrees.
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