1. 6-1 The Polygon Angle-Sum Theorems

2. Naming Polygons Polygons are named by the number of sides they have.
Type of polygon 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
n-gon

3. Finding a Polygon Angle Sum
Polygon Angle-Sum Theorem: The sum of the measures of the interior angles of an n-gon is (n – 2)180.
What is the sum of the interior angle measures of a heptagon?

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

5. Finding the Number of Sides of a Polygon
The sum of the interior angle measures of a polygon is How many sides does this polygon have?
The sum of the interior angle measures of a polygon is How many sides does this polygon have?

6. Using the Polygon Angle-Sum Theorem
What is mY in pentagon TODAY?

7.  What is mG?

8. Regular 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 Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is
What is the measure of each interior angle in a regular hexagon?

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

11. Exterior Angles
You can draw exterior angles at any vertex of a polygon.
Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon (one at each vertex) is 360.

12. Finding an Exterior Angle Measure
What is m1 in this regular octagon?

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