Clock Hands
3 August 2010
Clock Hands
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What is the measure of the angle formed by a clockâs hands at 10:20?
I'm very confused by this homework question. I got 170 degrees but I know that it is incorrect. Please help! Thanks 
Each hour/5min section on the clock face is 360/12 = 30 degrees.
The minute hand points to 4 which is 120 degrees after 12.
The hour hand has moved 1/3 hour past the 10
10 is 60 degrees before 12 so the hour hand is 50 degrees before the 12.
So what's wrong with 170 = 120 + 50 as the angle between the two hands?
I can do this another way.
At 10-00 the angle is 60 degrees
Each minute the minute hand moves forward 360/60 = 6 degrees.
Each minute the hour hand moves forward 30/60 = 0.5 degrees.
So each minute the angle increases by 5.5 degrees.
5.5 x 20 = 110 so the angle has increase by 110 degrees after 20 min.
The angle now is 60 + 110 = 170.
