How Can The Internal Angles Of A Polygon Be Found?

The interior angles of a polygon are the angles at each vertex on the inside of the polygon. They always lie inside the polygon and can be calculated using three methods: finding the sum of interior angles, finding the measure of one interior angle, and finding the value of the interior angle of a regular polygon.

For example, a triangle has 5 interior angles of 108^o and 5 exterior angles of 72^@, with the exterior angles having a sum of 360^@ =72^@. To find the value of the interior angle of a regular polygon, the formula for finding the sum of interior angles is (n – 2) * 180.

To find the measure of one interior angle, divide the formula by the number of sides n: (n – 2) * 180 / n. For each angle in a regular polygon, the sum of interior angles is (n – 2) × 180° / n. A regular polygon has all its interior angles equal to each other, such as a square having all its interior angles equal to the right angle or 90 degrees.

To calculate the sum of the interior angles of a polygon, split it into triangles and multiply the number of triangles by 180°. In a triangle, the sum of interior angles is 180°. To find the value of the interior angle of a regular polygon, multiply the number of triangles in the polygon by 180°.