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.