The measure of the central angle of a circle is equal to the measure of…
Its intercepted arc
…the intercepted arc that it subtends. In other words, if you draw two radii of a circle to the endpoints of an arc, the angle between those radii (the central angle) will have the same measure as the arc that it cuts off from the rest of the circle.
Conversely, given a central angle of a circle, you can find the measure of the corresponding intercepted arc by simply setting the two measures equal to each other. For example, if a central angle measures 60 degrees, then the intercepted arc also measures 60 degrees.
This relationship between central angles and intercepted arcs is key to many important concepts in geometry and trigonometry, including the law of sines and the area of a sector of a circle.
More Answers:
Diving into the Basics of Chords: Understanding Triads, Major, Minor, Augmented, and Diminished Chords in Western MusicTangent-Secant Theorem: Proving Equal Length Segments in Circles
Learn How to Find the Equation of a Tangent Line in Calculus
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded