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.)


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.


Try this:

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

Use the formula (n-2)*180 degrees.

(10-2)*180 degrees

8*180 degrees

1464 degrees


Try these on your sheet of paper.

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!


The Million Dollar Question:

In what real world situations would this theorem be useful?

Let me know what you think. Leslie Giambalvo

To go back to the Polygons.