The formula for the sum of the interior angles of a polygon is

,

where is the number of sides in the polygon

Plugging in our values, we get:

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

The following equation can be used to determine the measure of an interior angle of a regular polygon, where equals the number of sides.

In a pentagon, .

Now we can solve for the angle.

To find the angle of any regular polygon you find the number of sides . For a pentagon, .

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon.

Then to find one individual angle we divide 540 by the total number of angles 5,

The answer is .

The measure of an interior angle of a regular polygon can be determined using the following equation, where equals the number of sides: