Problem:
What is the measure of the acute angle formed by the hands of a clock at a.m.?
Answer Choices:
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Solution:
Note that in the same period of time, the hour hand moves as far as the minute hand. At a.m., the minute hand is at and the hour hand is at . By a.m., the minute hand has moved of way around the clock to , and the hour hand has moved of the way around the clock from . Therefore, the angle formed by the hands at a.m. is .
As the minute hand moves of the way around the clock face from to , the hour hand will move of the way from to . So the hour hand will move of of , or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions