Investigate Polygon Interior Angle Sum

Question:

What is the sum of the measures of the interior angle of a convex n-gon?

Explore:

1. In each polygon, draw all the diagonals from one vertex. Notice that the diagonals divide the polygon into triangles.[br][br]2. By the Triangle Angle Sum Theorem, the sum of the interior angles of a triangle is [math]180^o[/math]. Use this theorem to complete the table.

Investigating Polygon Interior Angle Sum

Based on the data in your table, which of the following expressions would you use to determine the number of triangles in an n-gon?

[math]n+1[/math] [math]n+2[/math] [math]n-2[/math] [math]n-1[/math]

Based on the data in your table, which of the following expressions would you use to determine the sum of the measures of the interior angles of an n-gon?

[math]\left(n-3\right)\cdot180[/math] [math]\left(n+3\right)\cdot180[/math] [math]\left(n+2\right)\cdot180[/math] [math]\left(n-2\right)\cdot180[/math]

Information: Investigate Polygon Interior Angle Sum