In the above figure, the angles a, b, c, d, e and f are the central angles of the hexagon. There are 6 central angles in a hexagon. The number of central angles in a polygon is always equal to the number of sides of the polygon.

As you can see in the figure above, all the central angles of the polygon together will always form a complete circle. Hence the central angles add up to 360° in all polygons. Since a regular polygon has all equal sides, the central angles in a regular polygon are also equal.

So to find the measure of the central angles of a regular polygon follow the steps below:

First identify the number of sides ‘n’.

Then divide 360° by n.

For example: say you need to find the central angle of a regular pentagon.

First identify the number of sides ‘n’: here n = 5

Then divide 360° by n: 360° ÷ 5 = 72°.

Conversely, you can also find the number of sides of a regular polygon, when the central angle is given, by dividing 360 by the central angle.

Note: In the case of an irregular polygon, since there is no clear center for an irregular polygon, it has no central angle.

3 0

2 years ago