7.4 Regular Polygons7.4 Regular Polygons

Recognize regular polygons

Use formulas to find measure of an exterior angle of an equiangular polygon

Regular Polygons:Equilateral and equiangularRegular Polygons:Equilateral and equiangular

T58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula

E = 360n

Find m<1 in the figure below

1

m<1 = 3605

m<1 = 72

T58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula

E = 360n

Problems:

1. How many degrees in each exterior < of an equiangular heptagon?

E = 3607

= 51 3/7

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

E = 360n

18 = 360n

18n = 360

n = 20 sides

Plug in 18 for E

Multiply both sides by n

Divide by 18

3. If each angle of a polygon is 108, how many sides does it have?

First find the exterior angle.

180 - 108 = 72

Set up with correct formula:

E = 360n

solve

Remember to show your work!Remember to show your work!

72 = n

360

72n = 360

n = 5

The shape has 5 sides.

Given the stop sign shown, is NTE scalene, isosceles, equilateral or undetermined?

O I

N T

S

EU

Q

isosceles