Central Angles: How To Calculate Arc Length And Sector Area In A Circle

Central angle

angle whose vertex is the center of the circle and whose sides are radii of the circle

A central angle is an angle formed by two radii of a circle, with the vertex of the angle located at the center of the circle. In other words, if you imagine a segment connecting the center of a circle to two points on the circumference, the angle between those two segments is a central angle.

Central angles are measured in degrees or radians and can be used to calculate the arc length or sector area of a corresponding section of a circle. Furthermore, the measure of a central angle is also equal to the measure of the arc it intercepts, provided that both measurements are in the same units.

For example, if a central angle measures 60 degrees, then the corresponding arc length would be 60/360 of the full circumference of the circle or one-sixth of the circle’s circumference. Similarly, if the circle’s radius is known, the measure of a central angle can be used to calculate the area of the corresponding sector of the circle.

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