1. Angle Measures in Polygons
Geometry

2. Polygon Angle Measures
# of sides
# of congruent triangles
Sum of measures of interior angles
TRIANGLE
QUADRILATERAL
PENTAGON
HEXAGON
…..
N-GON

3. POLYGON INTERIOR ANGLES THEOREM
The sum of the measures of the interior angles of a convex n-gon is… (n – 2) · 180

4. Regular Polygons
What is the difference between a polygon and a regular polygon?

5. More Regular Polygons

6. COROLLARY TO THEOREM 11.1

7. Example

8. Find the value of x in the diagram.
Example
Find the value of x in the diagram.
114°
105° x°
135°
102°

9. Example
The measure of each interior angle of a regular polygon is 140°. How many sides does the polygon have?

10. Example
The measure of each interior angle of a regular polygon is 165 degrees. How many sides does the polygon have?

11. Examples
A heptagon has four interior angles that measure 160 degrees each and two interior angles that are right angles. What is the measure of the other interior angle?
Find the measure of each angle in a regular 11-gon.

12. Interior vs Exterior

13. Walk around the polygon
Exterior Angles
Walk around the polygon

14. POLYGON EXTERIOR ANGLES THEOREM
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

15. COROLLARY TO THEOREM 11.2

16. Example

17. Find x

18. Example
The measure of each exterior angle of a regular polygon is 40 degrees. How many sides does the polygon have?

19. Example
The sign on a building has a long narrow hexagon shape. Four of the interior angles measure 140 degrees each. The remaining two interior angles at each end of the sign are congruent. What is the measure of each angle.

20. Example
If you were designing a sign for a new building, would it be possible to make a sign that is a regular polygon with each angle having a measure of…. a. 160 degrees b. 115 degrees