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7.4 Regular Polygons. Recognize regular polygons Use formulas to find measure of an exterior angle of an equiangular polygon. Regular 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 = 360.

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7 4 regular polygons

7.4 Regular Polygons

Recognize regular polygons

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

slide3
T58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula
  • E = 360

n

slide4

Find m<1 in the figure below

m<1 = 360

5

m<1 = 72

1

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

E = 360

n

slide5

Problems:

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

E = 360

7

= 51 3/7

slide6

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

E = 360

n

18 = 360

Plug in 18 for E

n

18n = 360

Multiply both sides by n

n = 20 sides

Divide by 18

slide7

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 = 360

n

solve

remember to show your work
Remember to show your work!

72 =

72n = 360

n = 5

The shape has 5 sides.

slide9

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

O

I

T

N

isosceles

S

Q

U

E