SOLUTION: What is the exact degree measure of the angle formed by the hands of a clock at 2:40?

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!
email me and I'll talk you through this one
.
justin.sheppard.tech@hotmail.com
Answer by richwmiller(17219)   (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
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

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.

John

Answer by Alan3354(69443)   (Show Source): 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)
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