Definition: The angle
subtended
at the
center of the polygon
by one of its sides.

Try this Adjust the number of sides of the polygon below, or drag a vertex
to note the central angle of the polygon.

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. The angle depends only on the number of sides, not the size of the polygon. If you change the number of sides, you will see that as the number of sides gets larger, the cenral angle gets smaller.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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