Download 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.
Regular 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 ___________
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.
360
m1 
 72
5
Theorem
The measure ___ of each _______
angle of an equiangular polygon of n
sides is given by the formula
360
E
n
Example 1
How many degrees are there in each
exterior angle of an equiangular
heptagon?
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?
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
Summary
Explain why the statement “If a
polygon is equiangular, then it is a
regular polygon” is false.
Homework
Worksheet 7.4