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Concept

Central Angle

An angle whose vertex lies at the center of a circle and whose legs are radii is called a central angle.

In this diagram, ∠ C is a central angle of the circle. Note that the measure of the intercepted arc of a central angle is equal to the measure of the central angle.

Why

Recall that both a circle and a complete angle measure 360 degrees. Since the vertex of a central angle lies at the center of a circle, both the central angle and its intercepted arc represent the same portion of the circle. Use the slider in the applet to see this relationship.

Therefore, the central angle and its intercepted arc have the same measure.

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