Regular polygons have all sides, and all angles equal.
Size of Internal Angles
To find the size of the internal angles of a regular polygon with ‘n’ sides, use the formula:
For example, the size of the interior angles of the pentagon (five sides) above is:
The sum of all the interior angles of a polygon with ‘n’ sides is found using the formula:
(n – 2) x 180°
Therefore, the sum of all the interior angles of the pentagon above is:
(5 – 2) x 180° = 3 x 180° = 540°
Size of Exterior Angles
Interior and Exterior angles are measured on the same line, that is, they add up to 180°.
Therefore, the size of an exterior angle = 180° – Interior angle.
For example, the size of the external angle of the pentagon above is:
Since, interior angle = 108°
Then, exterior angle = 180° – Interior angle
180° – 108° = 72°
Below is a list of the names and the number of sides, of some of the most popular polygons.
|Name of Polygon||Number of Sides|