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You have just been talking about limits and discrete values. Be sure to continue to use these words when appropriate to reinforce their meaning and their recurrence.

Time Estimate


Main Idea

10-15 min


Given a polygon, what would be the angle sum? Given a sum or given an angle, what would be the polygon? Give some angle sums with no solution.

You can use a formula in both directions.

Not all problems have a solution.

20 min


In groups, create non-regular polygons of given numbers of sides for the non-regular table. Does it still work?

Testing the formula for angle sums to non-regular polygons.

Step-by-step guide:

1. Provide an example of a polygon. Ask the participants to name the angle sum of that polygon. (Triangle, angle sum = 180º ; Octagon, angle sum = 1080º)

2. 1120º —> no meaningful solution

3. 1260º —> nonagon

4. Each angle has degree measure of 120º —> hexagon

5. Each angle has degree measure of 108º —> pentagon Each angle has degree of 85º—> no meaningful solution

Possible Problems and Concerns:

Internet Resources:

There is a Sketchpad file of a regular 20-gon at https://mste.illinois.edu/m2t2algebra/20gon.gsp

Have students write scripts to build regular polygons.

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