Investigating the Sum of Interior Angles of Polygons

A polygon can be divided into a number of triangles by joining one vertex to the rest of the vertices by straight lines. Since the sum of internal angles of a triangle is 180 degrees, the sum of the interior angles of the polygon will be equal to the number of inscribed triangles times 180.

1. In each of the polygons, pick one vertex and draw all of the diagonals from that vertex. Notice how this divides each polygon into triangular regions.

2. Make a conjecture about the sum of the interior angles of any convex polygon.

3. Draw your own polygons of any size and test your conjecture!

Priscilla Allan, 2 March 2014, Created with GeoGebra