Suggestion:
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

Activity

Main Idea

1015 min
(1:55)

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
(2:15)

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

Testing the formula for angle sums to
nonregular polygons.

Stepbystep 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 20gon at
https://mste.illinois.edu/m2t2algebra/20gon.gsp
Have students write scripts to build regular
polygons.
