1. Angle Measures in Polygons Chapter 11, Section 1 June 23, 2016

2. Goals To find the measures of interior and exterior angles of polygons. To use measures of angles of polygons to solve real-life problems.

3. Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2) 180. (COROLLARY) The measure of each interior angle of a regular n-gon is (n-2) 180 n

4. Example 1 – Finding Measures of Interior Angles of Polygons Find the value of x in the diagram shown. 114º 105º 135º XºXº 102º

5. Example 2 – Finding the Number of Sides of a Polygon The measure of each interior angle of a regular polygon is 165º. How many sides does the polygon have?

6. Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360º. 1 2 3 4 5

7. (COROLLARY) The measure of each exterior angle of a regular n-gon is 360º. n

8. Example 3a – Finding the Measure of an Exterior Angle Find the value of the variable in the diagram. yºyº 2yº yºyº

9. Example 3b Find the value of the variable in the diagram. xºxº

10. Example 4 – Finding Angle Measures of a Polygon The sign on a building has a long narrow hexagon shape. Four of the interior angles measure 140º each. The remaining two interior angles at each end of the sign are congruent. What is the measure of each angle?

11. Example 5 – Using Angle Measures of a Regular Polygon 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) 160º ? B) 115º ?

12. Homework Pg 665 #’s 1-25 all