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# Why is it not 120?

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What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock?

Sep 15, 2018

### 3+0 Answers

#1
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Use this formula to calculate the angle between the two hands of a clock.
Abs(1/2 * (60*H) - (11*M)) =, whrere H=Hours, M=Minutes.
Abs(1/2 * ((60*2) - (11*30)) =
Abs(1/2 * (120 - 330) =
Abs(1/2 * (210)=105 degrees

Sep 15, 2018
#2
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Hour hand moves 360 degrees in 12 hours  ....   30 degrees per hour or 15 degrees per 1/2 hour

so 2:30  would be 5    1/2 hour segments   5 x 15 = 75 degrees= angle of hour hand.    The MINUTE hand will be at 180 degrees (pointing directly downwawrd)      180 degrees - 75 degrees = 105 degrees.

Sep 15, 2018
#3
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What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock?

At 2:30 the big hand is on the 6 hour mark and the little hand is half way between the 2 and the 3

The clock is divided into 12 hourly segments so each segment is 360/12 = 30 degrees

the hands are 3.5 segments apart

3.5*30 =  105 degrees

Sep 16, 2018