1. Then: You name and classified polygons Now: 1.Find and use the sum of the measures of the interior angles of a polygon. 2.Find and use the sum of the measures of the exterior angles of a polygon. One-Patch Quilt 6.1 ANGLES OF POLYGONS http://0.tqn.com/d/quilting/1/0/f/d/-/-/gpa-veg-patch.jpg

2. Polygon Number of Sides Number of triangles Sum of measures of interior angles Triangle 31 1 x 180  = 180  Quadrilateral Pentagon Hexagon INVESTIGATE ANGLE SUMS IN POLYGONS

3. Conclusions 1.Pattern: 2.Expression: 3.Side lengths affect the sum? INVESTIGATE ANGLE SUMS IN POLYGONS

4. The sum of the interior angles of an n-sided convex polygon is (n-2) x 180. Example: m  A + m  B + m  C + m  D + m  E + m  F = (6-2)(180) = 720 THEOREM 6.1: POLYGON ANGLES SUM http://image.tutorvista.com/calc_images/image/math/polygon.jpeg

5. a.Find the sum of the measures of the interior angles of a convex heptagon. b.Find the sum of the measures of the interior angles of a convex 15-gon. EXAMPLE 1 A: FIND THE INTERIOR ANGLES SUM

6. a.Find the sum of the interior angles. b. Solve for x. c. Find the measure of each angle. EXAMPLE 1 B: FIND THE MEASURE OF EACH INTERIOR ANGLE http://moodle.tbaisd.org/pluginfile.php/68876/mod_book/cha pter/50999/angle%20sum%20ex.jpg

7. a.Find the sum of the interior angles. b. Solve for x. c. Find the measure of each angle. EXAMPLE 1 C: FIND THE MEASURE OF EACH INTERIOR ANGLE

8. ARCHITECTURE A mall is designed so that five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon. EXAMPLE 2 A: INTERIOR ANGLES MEASURE OF REGULAR POLYGONS

9. for a regular dodecagon EXAMPLE 2 B: FIND THE MEASURE OF EACH INTERIOR ANGLE http://www.gazebocreations.com/images/ProductPrope rtySet/225x177/Gazebos-dodecagon-red-cedar-single- roof.jpg

10. Sum of interior angles = (n – 2) x 180 Regular polygon: Each angle of regular polygon x n = (n – 2) x 180 The measure of an interior angle of a regular polygon is 150. Find the number of sides. EXAMPLE 3: FIND THE NUMBER OF SIDES OF A REGULAR POLYGON

11. The sum of the exterior angle measures of a convex polygon, one at each vertex, is 360. Example: m  1 + m  2 + m  3 + m  4 + m  5 = 360 THEOREM 6.2 POLYGON EXTERIOR ANGLES SUM

12. a.Find the value of x. EXAMPLE 4: FIND THE EXTERIOR ANGLE MEASURES OF A POLYGON

13. b. Find the measure of each exterior angle of a regular dodecagon. EXAMPLE 4:

14. p. 398-401 #12-24 evens, 25, 26-34 evens, 38, 40, 44, 46, 47, 54 6.1 ASSIGNMENT: