I kinda like the explanation given here:

http://www.coolmath.com/lesson-interior-angles-of-polygons-1.htm

It is a nice middle school level of explanation for the kids.

Leslie

Leslie Damon
VTC Instructor, Computer and Information Science
(and former middle level math teacher)

They show two different ways of thinking about it
On Mar 10, 2010, at 9:29 AM, CAROL MCNAIR wrote:

> I have been thinking about an question, and can't find the answer.   
> Is there anyone who might know?  I am trying to determine WHY the  
> formula (n-2)(180) works for finding sum of interior angles of  
> regular polygons.  Is it because 1 line is a straight line with 180  
> degrees, and then adding additional lines add 180 degrees, hence a  
> triangle with 3 sides is (3-2)(180)?
>
>
> Carol McNair
> Team Sequoia
> Camels Hump Middle School
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