The measure of each exterior angle of a regular polygon is 72 degrees. how many sides does the polygon have?

If the measure of each exterior angle is 72, the measure of each interior angle is then 180-72=108

the sum of the interior angles of a polygon is (n-2) * 180, n is the number of sides

(n-2) * 180=108*n

180n-360=108n

180n-108n=360

n=5

the polygon has 5 sides.