Angle Measure

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This Demonstration shows the measure of an angle in degrees and radians.

Contributed by: Frederick Wu (March 2011)
Additional contributions by: Bing Ye
Open content licensed under CC BY-NC-SA



In order to measure an angle , a circular arc centered at the vertex of the angle is drawn. The length of the arc is then divided by the radius of the circle , and possibly multiplied by a scaling constant (which depends on the units of measurement that are chosen): .

The value of thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio is unaltered.

Angles are usually measured in units of degrees or radians.

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