How To Find The Interior Angle Of A Polygon

A polygon is called a regular polygon when all of its sides are of the same length and all of its angles are of the same measure.

How to find the interior angle of a polygon. The interior and exterior angles together lie on a straight line. Polygons interior angles theorem. After examining we can see that the number of triangles is two less than the number of sides always.

The sum of interior angles of a regular polygon and irregular polygon examples is given below. In a polygon of n sides the sum of the interior angles is equal to 2n 4 90. So you would use the formula n 2 x 180 where n is the number of sides in the polygon.

Sum of interior angles n 2 180 each angle of a regular polygon n 2 180 n. Remember that the sum of the interior angles of a polygon is given by the formula sum of interior angles 180 n 2 where n the number of sides in the polygon. The measure of each interior angle of a regular polygon is equal to the sum of interior angles of a regular polygon divided by the number of sides.

The formula for finding the sum of the interior angles of a polygon is the same whether the polygon is regular or irregular. The angle sum of this polygon for interior angles can be determined on multiplying the number of triangles by 180. An interior angle of a polygon is an angle inside the polygon at one of its vertices.

One way to find the sum of the interior angles of a polygon is to divide the polygon into triangles. If we know the sum of all the interior angles of a regular polygon we can obtain the interior angle by dividing the sum by the number of sides. Below is the proof for the polygon interior angle sum theorem.

In order to find the measure of a single interior angle of a regular polygon a polygon with sides of equal length and angles of equal measure with n sides we calculate the sum interior angles or n 2 180 and then divide that sum by the number of sides or n. Hence we can say now if a convex polygon has n sides then the sum of its interior angle is given by the following formula. Angle q is an interior angle of quadrilateral quad.