1. 6-1 The Polygon Angle-Sum Theorems

2. Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of a n-gon is 𝑛−2 180

3. NUMBER OF SIDES
NAME 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon

4. Problem 1: Finding a Polygon Angle Sum
What is the sum of the interior angle measures of a heptagon?

5. What is the sum of the interior angle measures of a 17-gon?

6. The sum of the interior angle measures of a polygon is 1980
The sum of the interior angle measures of a polygon is How can you find the number of sides in the polygon?

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

11. Problem 2: Using the Polygon Angle-Sum Theorem
The common housefly has eyes that consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in on hexagonal facet?

12. What is the measure of each interior angle in a regular nonagon?

13. Problem 3: Using the Polygon Angle-Sum Theorem

15. You can draw exterior angles at any vertex of a polygon
You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of the exterior angles, one at each vertex is 360.

16. Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For the pentagon

17. Problem 4: Finding an Exterior Angle Measure

18. What is the measure of an exterior angle of a regular nonagon?