What does a central angle equal in relation to its intercepted arc?

A central angle is defined as an angle whose vertex is at the center of a circle and whose sides extend to the circle itself. The arc that is intercepted by this central angle is the part of the circle that lies between the two points where the sides of the angle intersect the circle.

In geometric terms, the measure of a central angle is always equal to the measure of its intercepted arc. This relationship arises from the way circles are defined and measured, specifically using degrees or radians for both angles and arcs. Thus, for any given central angle, if you measure the angle in degrees, you will find that it is exactly the same measure as the angle represented by the arc it intercepts on the circumference of the circle.

This principle is fundamental in circle geometry and is essential for understanding more complex relationships involving angles and arcs in both theoretical and practical applications.