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.
2. By the Triangle Angle Sum Theorem, the sum of the interior angles of a triangle is . 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?
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?
Extended Learning
In a regular polygon, all interior angles are the same measurement. Knowing this, how can we find the measure of a specific interior angle of a regular polygon?