Central angle
Central angles are subtended by an arc between those two points, and the arc length is the central angle (measured in radians). The central angle is also known as the arc's angular distance.
The size of a central angle Θ is 0°<Θ<360° оr 0<Θ<2π (radians). When defining or drawing a central angle, in addition to specifying the points A and B, one must specify whether the angle being defined is the convex angle (<180°) or the reflex angle (>180°). Equivalently, one must specify whether the movement from point A to point B is clockwise or counterclockwise.
Let L be the minor arc of the circle between points A and B, and let R be the radius of the circle.
Proof (for degrees): The circumference of a circle with radius R is 2πR, and the minor arc L is the (Θ/360°) proportional part of the whole circumference (see arc). So:
Proof (for radians): The circumference of a circle with radius R is 2πR, and the minor arc L is the (Θ/2π) proportional part of the whole circumference (see arc). So
A regular polygon with n sides has a circumscribed circle upon which all its vertices lie, and the center of the circle is also the center of the polygon. The central angle of the regular polygon is formed at the center by the radii to two adjacent vertices. The measure of this angle is
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