1. Regular Polygons Lesson 7.4: Recognize regular polygons.
Use formulas to find measure of an exterior angle of an equiangular polygon.

2. Define regular polygon…

3. Regular Polygons: Equilateral and equiangular

4. Theorem 58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula
E = 360 n

5. m1 = 360 5 m1 = 72 Find m1 in the figure below
Theorem 58: The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula
E = 360 n

6. Problem #1:
1. How many degrees in each exterior  of an equiangular heptagon?
E = 360 7
= 51 3/7

7. Problem #2:
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

8. First find the exterior angle.
Problem #3:
3. If each angle of a polygon is 108, how many sides does it have?
First find the exterior angle.
180º - 108º = 72º
Set up with correct formula:
E = 360
72n = 360
n = 5
The polygon has 5 sides. n

9. Problem #4:
4. Given the stop sign shown, is NTE scalene, isosceles, equilateral or undetermined? O I T
Isosceles N S Q U E