1. Angle Measures of Polygons
Chapter 8 Section 1
Angle Measures of Polygons

2. Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is:

3. Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is:

4. Applying the Polygon Interior Angles Theorem
Sum of interior angles
Angle Measures if regular
Triangle (3-gon)
180o
60o
Quadrilateral
360o
90o
Pentagon
540o
108o
Hexagon
720o
120o
Octagon
1080o
135o
Decagon
1440o
144o
Dodecagon
1800o
150o
15-gon
2340o
156o

5. Example 1:
What is the sum of the interior angles of a convex nonagon?

6. Example 2:
We are told that a convex n-gon has an interior angle sum of 1620°. How many sides does the polygon have?

7. Example 3:
Find the measure of angle X from the polygon to the right.

8. What if we forget the formula?

9. Example 4:
Use triangles to determine the sum of the interior angles of this polygon.

10. Try these! 2. Find the measure of angle X below.
1. What is the interior angle sum of a convex 22-gon?

11. Exterior Angles of a Convex Polygon
The sum of the exterior angles, one at each vertex, of a convex polygon is:

12. Exterior Angles of a Convex Polygon
The sum of the exterior angles, one at each vertex, of a convex polygon is:

13. Example 4:
Solve for x in the following diagram:

14. Workbook Page 145-146 #16-21, 22-34even
Homework
Workbook Page #16-21, 22-34even