Question 254248: What is the exact degree measure of the angle formed by the hands of a clock at 2:40? Found 4 solutions by MRperkins, richwmiller, solver91311, Alan3354:Answer by MRperkins(300) (Show Source):
You can put this solution on YOUR website! That is a good one because the hands are not exactly on the 2 but are exactly on the 8.
How far off the 2 is the hour hand 40/60=2/3 between the 2 and the 3
The hour hand is then at 1/12*360 +(2/3*1/12)*360
The minute hand is at 40/60*360
subtract the hour hand from the minute hand
If the hour hand remained on the 2 for the entire hour, then the angle formed at 2:40 would be 180 degrees. But the hour hand takes an hour to go from 2 to 3. 40 minutes is 2/3 hour, so when the minute hand points to the 8, meaning 40 minutes after the hour, the hour hand will have moved 2/3 of the way from the 2 to the 3. Since there are 12 numbered divisions on the 360 degree clock face, the angular difference between the 2 and the 3 (or any other two adjaceent numbers) is 30 degrees. 2/3 of 30 degrees is 20 degrees. 180 degrees minus 20 degrees is 160 degrees.
You can put this solution on YOUR website! What is the exact degree measure of the angle formed by the hands of a clock at 2:40?
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The minute hand is (2/3)*360 from 12, = 240 degs
The hour hand is (2 2/3)*30 from 12 = 80 degs
diff = 160 degs (from the hour hand to the minute hand clockwise)
