Regular Polygons - Central, Interior, and Exterior Angles

• Protractor
• Ruler
• Printout of this activity OR print the PDF file of this activity.
  Print a set of Regular Polygons for your investigation!

1. A Regular Polygon is ___________________________________________. Use the printout figures along with your protractor to perform the following investigations.
2. Explore the relationship of the number of sides of a regular polygon and the Central Angles. Fill in the following table and make a generalization about Regular N-gons.

Name	# of Sides	Measure of a Central Angle	Sum of the Measure of the Central Angles
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Regular Octagon
Regular Decagon
Regular Dodecagon
Regular N-gon

3. Write a conjecture about the Central Angles of a Regular Polygon.
4. Explore the relationship of the number of sides of a regular polygon and the Interior Angles. Fill in the following table and make a generalization about Regular N-gons.

Name	# of Sides	Measure of an Interior Angle	Sum of the Measure of the Interior Angles
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Regular Octagon
Regular Decagon
Regular Dodecagon
Regular N-gon

5. Write a conjecture about Interior Angles of a Regular Polygon. Think about breaking apart the polygon into triangles as shown below.


Notice there are _______ triangles and the sum of the measures of the angles of each triangle is _______.

6. Explore the relationship of the number of sides of a regular polygon and the Exterior Angles. Fill in the following table and make a generalization about Regular N-gons.

Name	# of Sides	Measure of an Exterior Angle	Sum of the Measure of the Exterior Angles
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Regular Octagon
Regular Decagon
Regular Dodecagon
Regular N-gon



7. Write a conjecture about Exterior Angles of a Regular Polygons.
8. EXTENSION: What is the area of a regular n-gon?

Copyright 1998 by Margo Lynn Mankus