What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90?

- The sum of the exterior angles of a polygon is ALWAYS equal to 360 degrees. - The number of sides of the polygon is always equal to 360 / by the exterior angle. 
- A regular polygon is assumed (equal sides and equal angles all around). 
- Each exterior angle of a polygon is the supplement of its corresponding interior angle. 
- The sum of the interior angles of a polygon is equal to (n-2)*180. 
- It is also equal to the number of sides times each interior angle. 

360/90 = 4 (there are four sides)
supplementary = add up to get 180 degrees. Therefore, if the exterior and interior corresponding angles are supplementary, and all of the exterior angles are 90 degrees (because we are working with a regular polygon), all of the interior angles will also be 90 degrees.
* the sum of the interior angles of a polygon is equal to (n-2)*180. OR the number of sides multiplied by each interior angle.
PLUG IN... (4-2) * 180 -> 360 degrees.

number of sides = 4 (as previously determined) multiplied by the average of the interior angles... Since all interior angles are 90 degrees, the answer is able to be checked accurately.

The sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90 is 360 degrees.