1. Polygons Advanced Geometry Polygons Lesson 1

2. Polygon a closed figure Examples NO HOLES NO CURVES SIDES CANNOT OVERLAP all sides are segments

3. connects any two nonconsecutive vertices Diagonal All diagonals Diagonals from one vertex

4. Convex Polygon # of Sides # of Triangles triangle quadrilateral pentagon octagon n-gon 3 4 5 8 n 1 2 3 6 n - 2 Sum of Interior Angle Measures Formula for the Sum of the Measures of the Interior Angles 180(n - 2) 180° 360° 540° 1080° n - 2

5. Example: Find the sum of the measures of the interior angles of a convex 23-gon.

6. Example: Find the measure of each interior angle.

7. If a polygon is regular, the measure of each interior angle can be found. One Angle of a Regular Polygon Sum of the Interior Angles Number of Angles

8. Example: Find the measure of one interior angle of a regular nonagon.

9. Example: The measure of an interior angle of a regular polygon is 135. Find the number of sides in the polygon.

10. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex is 360. Sum of the Measures of the Exterior Angles

11. Interior Angles Exterior Angles SUM ONE

12. Find the measures of one interior angle and one exterior angle of a regular heptagon. Example:

13. One interior angle and one exterior angle of a regular polygon will always be supplementary. Why? They form a linear pair.