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

Algebra ->  Algebra  -> Polygons -> SOLUTION: What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90?       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Polygons Solvers Lessons Answers archive Quiz In Depth

 Question 262803: What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90? Answer by Theo(3504)   (Show Source): You can put this solution on YOUR website!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. first example: sum of the interior angles of a regular triangle is (3-2) * 180 = 1 * 180 = 180. each interior angle of the triangle = 180/3 = 60 degrees. each exterior angle of the triangle = 180 - 60 = 120 degrees. 360 / 120 = 3 which is the number of sides of the triangle based on the exterior angle. next example: sum of the interior angles of a regular quadrilateral = (4-2) * 180 = 2 * 180 = 360. each interior angle of the quadrilateral = 90 degrees. each exterior angle of the quadrilateral = 180 - 90 = 90 degrees. number of sides of the quaqdrilateral = 360 / 90 = 4 based on the exterior angles. next example: sum of the interior angles of a regular pentagon = (5-2) * 180 = 3 * 180 = 540. each interior angle of the pentagon = 540/5 = 108 each exterior angle of the pentagon = 180 - 108 = 72. the number of sides of the pentagon = 360 / 72 = 5 based on the exterior angle. last example: sum of the interior angles of a regular hexagon = (6-2) * 180 = 4 * 180 = 720. each interior angle of the pentagon = 720/6 = 120. each exterior angle of the pentagon = 180 - 120 = 60. the number of sides of the hexagon = 360/60 = 6 based on the exterior angle. in your problem: you are given that the exterior angle = 90 degrees. take 360 and divide it by 90 and you get 4 sides to the polygon. each interior angle of the polygon = 180 - 90 = 90 degrees. 4 times 90 = 360 degrees. the sum of the interior angles of the polygon = 360 degrees. the polygon is a quadrilateral. the sum of the interior angles of a quadrilateral = (4-2) * 180 = 2 * 180 = 360. your answer is: the sum of the interior angles of a polygon = 360 if each exterior angle = 90 degrees.