SOLUTION: The sum of the interior angles of a regular polygon is 7560 degrees. Find the following: The number of sides is: The measure of each interior angle is: The measure of each ex

Algebra ->  Polygons -> SOLUTION: The sum of the interior angles of a regular polygon is 7560 degrees. Find the following: The number of sides is: The measure of each interior angle is: The measure of each ex      Log On


   



Question 584491: The sum of the interior angles of a regular polygon is 7560 degrees. Find the following:
The number of sides is:
The measure of each interior angle is:
The measure of each exterior and central angle is:
How would I solve this? I know how to solve it if I know the # of sides but not when it only gives you the sum of all of the interior angles.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of the exterior angles is 360º ___ so one would equal 360º/n

an interior angle is the supplement of an exterior ___ 180º - (360º / n)

n[180 - (360/n)] = 7560 ___ 180n - 360 = 7560 ___ 180n = 7200