THE POLYGON SUM THEOREM

The purpose of this page is to teach you the Polygon Sum Theorem.

The Triangle Sum Theorem states: The sum of the measures of the angles in a triangle is 180 degrees.

Since a convex quadrilateral is the sum of two triangles the sum of the measures of the angles in a convex quadrilateral is 180degrees + 180degrees.

What is the sum of the measures of the angles in a convex pentagon? (HINT: Break the pentagon into triangles.)

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Do you notice a pattern?

A PATTERN?

3-gon	1 *180degrees
4-gon	2 *180 degrees
5-gon	3 *180 degrees
6-gon	4 *180 degrees
7-gon	5 *180 degrees

Do you notice that the number multiplying 180 degrees is 2 less than the number of sides of the polygon?

Therefore, the thought is this:

The equation for the sum of the measures of the degrees of a convex polygon is (n-2)*180 degrees where "n" is the number of sides of the polygon. This thought was proven true. It is called the Polygon Sum Theorem.

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Try this:

What is the sum of the measures of the angles of a 10 sided convex polygon?

What is the sum of the measures of the angles of a 8 sided convex polygon?

What is the sum of the measures of the angles of a 20 sided convex polygon?

What is the sum of the measures of the angles of a 105 sided convex polygon?

Check your answers!

In what real world situations would this theorem be useful?

Let me know what you think. Leslie Giambalvo

To go back to the Polygons.