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What is the degree measure of the acute angle formed by the hands of a 12-hour clock...

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nadolla | Student, Undergraduate | eNoter

Posted January 20, 2011 at 11:44 AM via web

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What is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o’clock ?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 20, 2011 at 11:50 AM (Answer #1)

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When looking at the clock, we notice that the circumference is divided into 12 equal sections.

These sections represents the hours.

When the clock is exactly 1:00, the hands will be on the numbers 12 and 1.

Then, the angle between the hands will have the same ratio of the section on the circumference.

The section length between the 12 and the 1 is 1/12 of the circumference.

Then the angle between the hands will have the same ratio.

==> We know that the rotation of the circle is 360 degrees.

==> Then the angle is 1/12 of  360 degrees.

Then the angle = 1/12 * 360 = 30 degrees.

Then the acute angles between the hands is 30 degrees.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 20, 2011 at 11:53 AM (Answer #2)

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At exactly 1 o' clock , the minute hand is 12 and the hour hand is at 1.

In a clock the 360 degrees are divided by the 12 hours. So the angle between each number is 360/12 = 30 degrees

The angle formed by the hour hand at 1 and the minute hand at 12 is 30 degrees.

The required angle at 1 o' clock is 30 degrees.

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