What is the sum of the measure of the interior angles of a regular polygon if each exterior angle measures 72 degrees

Sum of interior and exterior angle is 180 so

Interior angle =180−72=108

Now we need to find the no of sides of the polygon= n We know that interior angle of n-sides is given by

(n−2)×180n

We have

(n−2)×180=108n

or

180n−360=108n

or

72n=360

n=5 sides so there are 5 angles each of 108 degrees Sum of the interior angles=108+108+108+108+108=540
To find the measure of each exterior angle of a regular polygon, you just divide 360 degrees by the number of sides.