Time Estimate Activity Main Idea 10 min (2:00) Partition your non-regular polygons into the minimum number of triangles using line segments from vertex to vertex. Justification of the formula for non-regular polygons. 15 min (2:15) Present the center-point situation and discuss "How would you, as a teacher, respond to this student's sum not fitting the triangle pattern (the angle sum formula).?" Anticipation of alternative solutions.
Step-by-step guide:

1. Have participants draw triangles to partition their polygons. Be sure to discuss the word partition. It is important in mathematics. The green lines on the irregular hexagon illustrate how this is done.

2. Show that another way to do this is to create a point inside the polygon and draw lines to the vertices. Notice that you must subtract 360 from result! The red lines on the irregular quadrilateral illustrate this.

Possible Problems and Concerns:
It is important participants use line segments from vertex to vertex to ensure that they are working with the minimum number of triangles per polygon. That is, they should not create new points on the sides.
Internet Resources:

http://www.mste.uiuc.edu/m2t2/algebra/nonregs2.gsp is a Geometer's Sketchpad file of the irregular polygons at the right.