1. 7.4 Regular polygons Objective:
After studying this section, you will be able to recognize regular polygons and use a formula to find the measure of an exterior angle of an equiangular polygon.

2. Regular Polygons: Notice anything in common between these polygons?
Equilateral
Triangle
Regular Pentagon
Square
Regular Hexagon
Notice anything in common between these polygons?
Definition:
A regular polygon is a polygon that is both _____________ and ___________

3. 1
In the last lesson you learned that the sum of the exterior angles is 360 for any polygon.
In a regular polygon all the angles inside are equal so the exterior angles should be equal as well.
If we take 360 and divide by 5 (there are 5 angles) we will get the measure of angle 1.

4. Theorem
The measure ___ of each _______ angle of an equiangular polygon of n sides is given by the formula

5. Example 1
How many degrees are there in each exterior angle of an equiangular heptagon?

6. Example 2
If each exterior angle of a polygon is 18 degrees, how many sides does the polygon have?
Example 3
If each angle of a polygon is 108 degrees, how many sides does the polygon have?

7. Find the measure of each angle of a regular octagon
Example 4
Find the measure of each angle of a regular octagon
Example 5
Find the measure of each exterior angle of an equilateral quadrilateral

8. Summary Homework Worksheet 7.4
Explain why the statement “If a polygon is equiangular, then it is a regular polygon” is false.
Homework
Worksheet 7.4