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Central Angle of a Polygon
Definition: The angle subtended at the center of the polygon by one of it's sides.
Try this Adjust the number of sides of the polygon below, or drag a vertex to note the central angle of the polygon.
(If there is no image below, see support page.)
Regular Polygon case
The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon. If you were to draw a line from any two adjacent vertices to the center, they would make the central angle. Because the polygon is regular, all central angles are equal. It does not matter which side you choose.

All central angles would add up to 360° (a full circle), so the measure of the central angle is 360 divided by the number of sides. Or, as a formula:

where
n  is the number of sides

The measure of the central angle thus depends only on the number of sides. In the figure above, resize the polygon and note that the central angle does not change. However, if you change the number of sides, it will change.

Irregular Polygon case
Irregular polygons are not considered as having a center, and so have no central angle.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons

(C) 2007 Copyright John Page