The measure of an exterior angle of a regular polygon is given below. find the measure of an interior angle. then find the number of sides. 72

Well we know that the exterior angle plus the interior angle is equal to 180.
In this case: 180-72=One interior angle.
180-72=108
Knowing that we can now find the number of sides. 
We know that the exterior angles have to add up to 360 and we know ht measure of one of the angles. We divide these numbers and we  can use this to solve for the number of sides.
360/72=number of sides
360/72=5
You have 5 sides and one interior angle measures 108 degrees.