Carol, If you take a polygon with 5 sides and divide it into triangles by connect a vertex to the other non-adjacent vertices, you will get only 3 triangles - no matter which way you do it.  Therefore you have 3 triangles, each with angles that add to 180.  If you take a polygon in general (with n sides), the number of triangles you can construct in this same manner you will end up with n-2 triangles.  With some diagrams, this becomes much more clear for students.  By the way it works for all polygons, not just regular polygons.
Rick Martin
Colchester Middle School

________________________________________
From: Middle Level Mathematics Network [[log in to unmask]] On Behalf Of CAROL MCNAIR [[log in to unmask]]
Sent: Wednesday, March 10, 2010 9:29 AM
To: [log in to unmask]
Subject: [MLMATHNET] I have a question

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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