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?

## 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.

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

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?

The Million Dollar Question:

In what real world situations would this theorem be useful?

Let me know what you think. Leslie Giambalvo