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?

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) (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:
degrees.
The sum of the exterior angles of a "regular" polygon with n sides is given by:
...and if you simplify this, you get...

degrees.
The measure of one interior angle of a "regular" polygon with n sides is:

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

The sum of all the interior and exterior angles is simply . If we subtract the total sum of the interior angles, we get , 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 .
RELATED QUESTIONS
what is the difference between finding the sum of the interior angles of a polygon and... (answered by solver91311)
If the sum of the interior angles of a polygon equals the sum of the exterior angles,... (answered by Alan3354)
The sum of the interior angles of a convex polygon is equal to the sum of the exterior... (answered by stanbon)
How many sides has a polygon in which the sum of the interior angles of the polygon is... (answered by Alan3354)
Interior angle of regular polygon is 3 times its exterior. a)find the size of exterior... (answered by solver91311)
The sum of the interior angles of a polygon is twice the sum of its exterior angles. How... (answered by Theo,ikleyn)
one exterior angle of a regular polygon measures 30 degrees. what is the sum of the... (answered by stanbon)
The sum of interior angles of a convex polygon is ten times the sum of its exterior... (answered by reviewermath)
I am a regular polygon with one exterior angle of 20 degrees. What is the sum of my... (answered by KMST)