Recall that the measure of each interior angle of a regular n -gon is ( n-2)180 n. To find the measure of an interior angle of a pentagon we have to substitute 5 for n in this expression.
( 5-2)180/5= 108
Measure of Exterior Angle
To find the measure of an exterior angle, notice that the interior and exterior angles of any polygon form a linear pair.
This means that their measures add to 180. Let's call the exterior angle of our regular polygon x. To find x, we can write an equation using the measure of the interior angle and the fact that these will add to 180.
108+x=180 ⇔ x=72
The measure of the exterior angle is 72.
