SOLUTION: What is the sum of the interior angles in a polygon? What is the sum of the exterior angles of a polygon? How do you find the measure of one angle of a polygon?

Algebra ->  Polygons -> SOLUTION: What is the sum of the interior angles in a polygon? What is the sum of the exterior angles of a polygon? How do you find the measure of one angle of a polygon?      Log On


   

Question 398123: What is the sum of the interior angles in a polygon?
What is the sum of the exterior angles of a polygon?
How do you find the measure of one angle of a polygon?
Found 2 solutions by Earlsdon, richard1234:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles of a polygon with n sides is given by:
S%5Bi%5D+=+%28n-2%29180 degrees.
The sum of the exterior angles of a "regular" polygon with n sides is given by:
S%5Be%5D+=+n%28180-%28%28n-2%29180%2Fn%29%29 ...and if you simplify this, you get...
S%5Be%5D+=+180n-180n%2B360
S%5Be%5D+=+360degrees.
The measure of one interior angle of a "regular" polygon with n sides is:
A%5Bi%5D+=+%28%28n-2%29%2A180%29%2Fn

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles is 180%28n-2%29 since you can draw n-2 non-overlapping triangles within the polygon.

The sum of all the interior and exterior angles is simply 180n. If we subtract the total sum of the interior angles, we get 180n+-+180%28n-2%29, or 360 degrees.

Not enough information for the third one, but the average measure is also the measure of an angle of a regular n-gon, or 180%28n-2%29%2Fn.