Well, the "hour" hand is 3.5 30=105 degrees from the "12" marking (30 degrees per hour), while the "minute" hand is 30 6=180 degrees from the "12" marking (6 degs per minute). The difference, that is, 75 degrees, is our angle. The other difference would have been over 180, which is not important for us.
At 3:30 , the minute hand is at number 6. At 3:00 the hour hand was at number 3. Now it has moved 15 degree. Hence the angle between the two is (90 -15) = 75 degree.
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At 3:30 P.M., the angle between the hour and minute hands of the clock is 75 degrees. The hour hand is at 105 degrees, while the minute hand is at 180 degrees. The difference between these two positions gives the angle.
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