1. 8.1 Angle measures of a Ploygon

2. Polygons Polygons are closed figures Made of strait segment Segments only intersect at endpoints forming vertices

3. Not a Polygon

4. Regular Polygon Convex All sides congruent all angles congruent

5. Interior and Exterior Angles

6. The sum of these is 180 degrees

7. Sum of the Exterior Angles Exterior angles of a convex polygon always add to 360

8. a and b are diagonals Diagonals are segments that join nonconsecutive vertices of a polygon

9. Finding the sum of the interior angles What is the sum of the angles of a triangle? What is the sum of the angles of a square? What about a pentagon?

10. The longer way to find the sum Cut the figure into nonoverlapping triangles Each triangle is 180 degrees. Triangles 180 degrees (1 triangle) Rectangle 360 degrees (2 triangles) Pentagon 540 degrees ( 3 triangles)

11. The short way Notice on all these figures the number of triangles is 2 less than the number of sides Sum of the interior angles can be expressed as S = (n-2)180 S= sum n = number of sides

12. Table of interior and exterior angles

13. Examples Find X 5 sides Use (n-2)180 to get 540 as the sum of the interior angles Subtract the angles given to get 117 as X

14. Example Find X The sum of the exterior angles is always 360 Subtract the angles you know to get 111

15. Example Find the measure of an interior and exterior angle of a regular decagon 10 sides 360 / 10 = 36 degrees for each exterior angle The sum of the interior and exterior angles is always 180 180 – 36 = 144 for each of the interior angles