Measure Of An Interior Angle

In a regular polygon all the interior angles are of the same measure.

Measure of an interior angle. The formula is where is the sum of the interior angles of the polygon and equals the number of sides in the polygon. The measure of each interior angle of an equiangular n gon is. The other part of the formula is a way to determine how many triangles the polygon can be divided into.

Though the sum of interior angles of a regular polygon and irregular polygon with the same number of sides the same the measure of each interior angle differs. If you count one exterior angle at each vertex the sum of the measures of the exterior angles of a polygon is always 360. The sum of the interior angles 2n 4 90 therefore the sum of n interior angles is 2n 4 90 so each interior angle of a regular polygon is 2n 4 90 n.

Set up the formula for finding the sum of the interior angles. 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 anglesor red n 2 cdot 180 and then divide that sum by the number of sides or red n. The sum of the measures of the interior angles of a polygon with n sides is n 2 180.

The value 180 comes from how many degrees are in a triangle. Color magenta i 180 n 2 n where i measure of each interior angle color white xxxxxx n number of sides replacing the values in the formula i 180 25 2 25. To find the measure of each interior angle first we need to find the sum of the measure of all interior angles and divide it by the number of sides.