Question 1144105
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There are many methods for solving this kind of problem.  What works for me is to find the measure of each of the hands with respect to 12:00.<br>
The hour hand moves 360 degrees in 12 hours, so its rate is 30 degrees per hour.<br>
The minute hand moves 360 degrees in 60 minutes, so its rate is 6 degrees per minute.<br>
At 11:10, the hour hand, measured from 12:00, has moved 30 degrees per hour for 11 1/6 hours, so 330+5 = 335 degrees.<br>
At 11:10, the minute hand, measured from 12:00, has moved 6 degrees per minute for 10 minutes, so 60 degrees.<br>
Then the larger angle between the two hands is 335-60 = 275 degrees; that makes the smaller angle 360-275 = 85 degrees.