1. [6-1] Polygon Angle-Sum Theorems
Mr. Joshua Doudt
Geometry (H)
12/8/2015

2. Objective
To find the sum of the measures of interior angles of a polygon
To find the sum of the measures of exterior angles of a polygon

3. Lesson Vocabulary Equilateral Polygon Equiangular Polygon
Regular Polygon

4. Essential Understanding
The sum of the interior angle measures of a polygon depedns on the number of sides the polygon has.
By dividing a polygon with n sides into (n-2) triangles, you can show that the sum of the interior angles measure of any polygon is multiple of 180

5. Theorem 6-1
The sum of the measures of the interior angles of an n-gon is (n-2)180.

6. Finding a polygon angle sum
What is the sum of the interior angle measures of a heptagon?
Sum = 𝑛−2 180
= 7−2 180
=5∗180
=900

7. Got it?
1a) What is the sum of the interior angle measures of 17-gon? Answer: b) The sum of the interior angle measures of a polygon is How can you find the number of sides in the polygon? Answer: 140

8. Polygons
An equilateral polygon is a polygon with all sides congruent. An equiangular polygon is a polygon with all angles congruent A regular polygon is a polygon that is both equilateral and equiangular.

9. Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is 𝑛−2 180 𝑛

10. Using Polygon Angle-Sum Theorem
The common housefly, Musca domestica, has eyes consists of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet?

11. Using the Polygon Angle-Sum Theorem
What is 𝑚∠𝑌 in pentagon TODAY?
110
120
150

12. 100 30 50
105 65 81
109

13. Theorem 6-2
The sum of the measures of the exterior angle of a polygon, one at each vertex is 360.

14. Finding an exterior angle measure
What is 𝑚∠𝑔 in the regular octagon at the bottom? 𝑚∠1= 𝑚∠1=45

15. Joke Time What kind of guns do bees use? BeeBee guns!
How much does a pirate pay for corn?
A buccaneer!
What happened when the butcher backed into his meat grinder?
He got a little behind in his work.

16. Homework
Pg 356
#7-25