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What is the angle formed by the hands of a clock at 1021?

Updated: 8/19/2019
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12y ago

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I like your question. The hour hand is 10/60 from vertical, which reduces to 1/6. Converting to degrees (there are 360 degrees in a circle), would mean 1/6 of 360, resulting in 60. 21 minutes from vertical is 21/60, but since degrees are 6 times more than minutes, the product of 21 and 6 is 126. The clockwise angle is therefore 60 + 126 = 186.

Since 186 is larger the a straight line, one might also answer that the angle formed on the Southwest side of the two hands is 174 (360 - 186). There are two angles formed by the hands in the circle.

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12y ago
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Q: What is the angle formed by the hands of a clock at 1021?
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What is the angle between the two hands of a clock when the time is 3 hours 35 minutes?

1021/2o There are 12 digits on the clock face => 3600 / 12 = 30o between each digit. As the minute hand makes one revolution, the hour hand only moves 30o. Thus when the minute hand as moved 35 mins past the hour, or 35/60 of a revolution, the hour hand will have moved 35/60 x 30o = 171/2o past the digit of the hour. Thus at 03:35 the minute hand will point to the 7 digit and the hour hand will point 171/2o past the 3 digit, or 121/2o before the 4 digit. So the angle between them is the angle between the 4 and 7 digits plus this bit extra = 3 x 30o + 121/2o = 1021/2o


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