1. Bell Ringer 1. Name all diagonals with an endpoint at vertex B. 2. Name all angles not adjacent to D. 3. Name the polygon. 2x + 2 The perimeter of the parallelogram is 84 feet. 4. Find the length of the base. 4x - 2

2. Polygon Interior Angles Theorem - the sum of the measures of the interior angles of a polygon with n sides is (n – 2)(180°)

3. Find the sum of the measures of the interior angles. 7 sides 10 sides 11 sides 9 sides 12 sides 16 sides 20 sides

4. Polygon Exterior Angles Theorem - the sum of the measures of the exterior angles, one at each vertex is 360°

5. Interior Angles Exterior Angles ? Exterior Angles of Polygons 180o Exterior angles of a polygon sum to 360o.

6. 72o 90o 108o 120o 72o 90o 90o 90o 60o 108o 108o Square Pentagon 72o 3 4 5 108o 72o 120o 108o 90o 90o 90o 60o 60o 120o 90o 72o Equilateral Triangle 45o 60o 45o 45o 60o 60o Octagon Hexagon 45o 45o 6 8 60o 60o 45o 45o 60o 45o Exterior Angles of Polygons Regular Polygons Interior angles are 180 – 45 = 135o Interior angles are 180 – 60 = 120o

7. Calculate the exterior and interior angles of each of these regular polygons. 2 4 3 1 7 sides 10 sides 11 sides 9 sides 6 7 5 12 sides 16 sides 20 sides Exterior Angles of Polygons Septagon/Heptagon Decagon Hendecagon Nonagon 51.4o/128.6o 40o/140o 36o/144o 32.7o/147.3o Icosagon Hexadecagon Dodecagon 18o/162o 22.5o/157.5o 30o/150o

8. Diagrams not accurately drawn Exterior Angles of Polygons Calculate the value of the unknown angles. 2 1 88o x 125o 115o w 108o z 80o 4 55o 3 ? 125o 45o 70o 65o 58o 32o y ? Angle w = 360 – (125 + 90) = 145o Angle x = 360 – (108 + 88 + 115) = 49o 55o 122o Angle z = 360 – (32 + 70 + 55 + 45 + 122) = 36o Angle y = 360 – (90 + 55 + 80 + 65) = 70o

9. Diagrams not accurately drawn You try! 1 2 110o 110o x w 85o 130o z y 4 63o 3 45o 55o 33o 115o 130o 58o 73o

10. What’s happened? (mathematically speaking) And finally: A hendecagon is laying eggsagons!