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.

Regular polygons: a few examples

EquilateralTriangle

Square

Regular Pentagon

Regular Hexagon

Notice anything in common between these polygons?

A regular polygon is a polygon that is both equilateral and equiangular

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.

1

If we take 360 and divide by 5 (there are 5 angles) we will get the measure of angle 1. 360

1 725

m

The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula

Theorem

360E

n

Example 1

How many degrees are there in each exterior angle of an equiangular heptagon?

Example 2

Example 3

If each exterior angle of a polygon is 18 degrees, how many sides does the polygon have?

If each angle of a polygon is 108 degrees, how many sides does the polygon have?

Example 4

Example 5

Find the measure of each angle of a regular octagon

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.

HomeworkWorksheet