Degree (Angle Measure)
Definition

"Degree" is a unit commonly used when measuring an angle. The symbol for degrees is "°".

The measure of an angle is a number representing the spread of the two arms of the angle.

Angle

360° is equivalent to one "revolution" (r). Given either a number of degrees or a number of revolutions, the other "unit" can be found by using equivalent ratios.


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An angle with a measure of 1° is shown in the the illustration below.

Angle

Benchmark Angle Measures

Common benchmark angles in degrees are usually either multiples of 90°, multiples of 45° or multiples of 30°, as shown below.

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Putting these together results in the following:

Angle

Note that the least common multiple of 30 and 45 is 90.


In the "grouped" diagram above there are "gaps" between 0° and 30°, 60° and 90°, 90° and 120°, etc.

These "gaps" occurs as the greatest common factor of 30 and 45 is 15 and the smallest benchmark angle is 30°.


Demonstration
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