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Time Estimate	Activity	Main Idea
20 min (2:35)	By groups, create non-regular polygons of given # of sides and have them measure the angles.	Testing the formula for angle sums to non-regular polygons.

The formula for the number of circle units is below. N is again a variable representing the number of sides on the polygon (regular or irregular, concave or convex).

Step-by-step guide:

1. Have the participants draw some irregular polygons.

2. Before they begin to measure, ask them if they thing their formula will still work if the polygons are not regular.

3. Mention that figures like the “bow-tie” are not polygons. At a later point, we will discuss why not.

4. Talk about the number of circle units that the angles of a polygon create. Is there a formula for this? Yes, it is (n-2)/2

Possible Problems and Concerns

 

Internet Resources:

The applet for the angle object is at https://mste.illinois.edu/users/exner/java.f/angleobject/