Understanding Central Angles | Definition, Measurement, and Applications in Circle Geometry

an angle with its vertex at the center of a circle and sides that are radii

An angle with its vertex at the center of a circle and sides that are radii is called a central angle

An angle with its vertex at the center of a circle and sides that are radii is called a central angle.

A central angle is formed by two radii (plural of radius) of a circle, with the vertex of the angle being at the center of the circle. The sides of the angle are the radii that intersect at the center.

The measure of a central angle is equal to the measure of the arc intercepted by the angle on the circumference of the circle. This means that if you know the measure of the central angle, you also know the measure of the arc it intercepts, and vice versa.

The measure of a central angle is typically given in degrees, with a full circle having a measurement of 360 degrees. Hence, a central angle that intercepts an arc of length equal to the radius of the circle would have a measure of 1 degree. Similarly, a central angle that intercepts an arc equal to half the circumference of the circle would have a measure of 180 degrees, which is a straight angle.

Central angles play an important role in understanding and calculating various properties of circles, such as arc length, sector area, and segment area.

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