Friday, August 24, 2012

Most of us know the sum of the degrees of the interior angles of a triangle and quadradrilateral are. But how do we determine the sum of the degrees of the interior angles of a pentagon, hexagon, ocotogan, etc? 

If n is the number of sides of the polygon, then (n - 2)180 is the sum of the interior angles of that polygon.

Therefore, the sum of the interior angles of a pentagon (5 sides) is (5 - 2)180 = 540

The sum of the interior angles of a hexagon (6 sides) is (6 - 2) 180 = 720

For a 7 sided polygon (7 - 2)180 = 900

and so on.

If the formula is hard to remember, you notice that as the number of sides increase, the sum increases by 180.

You may also want to note that the sum of the measures of the exterior angles of a polygon is always 360.


  1. The interior angles of a polygon are those angles at each vertex that are on the inside of the polygon. There is one per vertex. So for a polygon with N sides, there are N vertices and N interior angles.Completing the Square

  2. Yes Raj, that is correct, thanks for the post!