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Now we start looking at patterns in the structure of these regular polygons and their angles.


Important definitions:

Pattern: A pattern is a consistent form or method. Some patterns will jump out at you, others you have to look harder to see.

n-gon: An n-gon is a polygon with n sides.

variable: A variable is a symbol that represents a value or many possible values. (ex: "n" is a variable)

Time Estimate


Main Idea

10 min


Have several regular polygons on a worksheet. Measure angles and complete the table. Key question---what would be the angle for a "15-gon?"

Notice that when you multiply column one by column two, something great happens.

5 min


Say the pattern in words. What does this table reveal to us?

There may be various versions.

Step-by-step guide

1. Give everyone a worksheet with several regular polygons. (The worksheet may be found on the M2T2 page)

2. Allow participants time to measure the angles in each polygon and complete the table.

3. Ask questions about n-gons not provided. What would be the angle for a "15-gon?"

4. Ask participants to describe the patterns in words. Every time you add a side, you add 180 degrees! Why?

Possible Problems and Concerns:
Participants will notice that the angles are all equal and that the number of sides multiplied by one of the angles gives the angle sum. BUT, be sure they focus on the changes in the last column as you move to polygons with more sides.

Internet Resources:

https://mste.illinois.edu/m2t2/algebra/tableForPolygons.xls is an Excel spreadsheet with the table at the left. Participants can see the values, find the patterns and let the spreadsheet do the multiplication.

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