How to find an angle in a pentagon

The formula for the sum of the interior angles of any regular polygon is as follows:

where is equal to the number of sides of the regular polygon.

Therefore, the sum of the interior angles for a regular pentagon is:

To find the measure of one interior angle of a regular pentagon, simply divide by the number of sides (or number of interior angles):

The measure of one interior angle of a regular pentagon is 108 degrees.

By angle addition,

is one of two acute angles of isosceles right triangle , so .

To find we examine .

is an angle of a regular pentagon and has measure .

Also, since, in , sides , by the Isosceles Triangle Theorem, .

Since the angles of a triangle must total in measure,