1. Bellwork  If the measures of two angles of a triangle are 19 and 80, find the measure of the third angle  Solve (x-2)180=1980  Find the value of x x+3 58 No Clickers

2. Section 8.1

3. The Concept  By this point we’ve already discussed the special properties of triangles  Now we’re going to discuss some special properties of polygons and then further these with special properties of polygons

4. Definition Since we are discussing polygons that have more than three sides, we can now introduce the term…  Diagonal Segment that joins two nonconsecutive vertices Vertex Axis of symmetry

5. Geogebra Vertex Axis of symmetry Interior & Exterior Angles of polygons

6. Theorems Theorem 8.1: Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)180 Corollary to Theorem 8.1: Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360 o. Vertex Axis of symmetry

7. Example What is the sum of the interior angles of a decagon? Vertex Axis of symmetry

8. Example Find the measure of the missing angle? Vertex Axis of symmetry 115 65 155 130 95 x

9. Theorems Theorem 8.2: Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360 o. Vertex Axis of symmetry

10. Example Find the measure of the missing angle? 65 115 25 50 85 x No Clickers

11. Practical Example The base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior and exterior angle of the hexagon?

12. Homework  8.1 1, 2, 3-36 mult. 3

13. Example Solve for x? 101 95 3x+21 2x 161 177 163

14. Most Important Points  Definition of diagonal  Interior angles of a Polygon Theorem  Exterior angles of a Polygon Theorem