The Polygon Angle-Sum Theorem

1. The Polygon Angle-Sum Theorem

2. Check Skills You’ll Need Find the measure of each angle of quadrilateral ABCD. 32 45 30 55 65 70 25 87 61 55

3. Classifying Polygon A polygon is a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.

4. Name the polygon. Then Identify its vertices, sides , and angles. D H B K G M

5. A CONVEX polygon has no diagonal with points outside the polygon. A CONCAVE polygon has at least one diagonal with points outside the polygon

7. Complete the table

8. Theorem 3 – 9 Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is (n – 2)180.

9. Find the measure of the angle Y Y 135

10. Theorem 3 – 10 The sum of the measures of the exterior angles of a polygon, one at each vertex , 360. For the pentagon, m/_ 1 + m/_ 2 + m /_ 3 + m /_ 4 + m /_ 5 = 360 3 2 4 1 5

11. The game board whose figure is shown has the shape of a regular hexagon. It is packaged in a rectangular box outlined beneath it. The box uses four right triangles made of foam in its four corners. Find m/_ 1 in each foam triangle 2 2 1 1 1 1 2 2

12. End of discussion