Question 1188816
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There are many ways to set up this kind of problem for solving.  Here is the way I like best....<br>
I measure the number of degrees past "noon" that each of the hands of the clock has moved; then the angle between the hands is the difference of those two angles.<br>
At 3:30, the hour hand has moved 3.5 hours past noon at 30 degrees per hour (360 degrees in 12 hours), so it is 105 degrees past noon.<br>
At 3:30, the minute hand has clearly moved 180 degrees past noon.  However, to demonstrate the general solution method, it has moved for 30 minutes at 6 degrees per minute (360 degrees in 60 minutes), so it is 180 degrees past noon.<br>
So the angle between the two hands is 180-105 = 75 degrees.<br>