# Exterior Angles of Polygons Interior Angles Exterior Angles

Exterior Angles of Polygons Interior Angles Exterior Angles ? o 180 Use your protractor to measure the exterior angles of these shapes. Make a statement about your findings. Exterior angles of a polygon sum to 360o. Exterior Angles of Polygons 360o 72o 5 360o 90o 4 o 90 360o 120o o o 90 90o 3 90 Square Regular Polygons 120o 60o 72o 108 o 108Pentagon108

72oo 3 60o 60o 120 120o Equilateral Triangle 4 o 90o 90o 360 60o 6 Interior angles are 180 60 = 120o Hexagon 60o o 90o 60o 45o 6 60 o 60o 45o

60o 45o 45o o 45o 108 72o o 360o 45o 8 8 45 5 72o 45o Octagon 45o o 108 90o 60o o 72o Interior angles are 180 45 = 135o

Exterior Angles of Polygons Calculate the exterior and interior angles of each of these regular polygons. 2 1 3 7 sides 9 sides 4 10 sides to 1 dp 11 sides to 1 dp Septagon/Heptagon Nonagon Decagon Hendecagon 51.4o/128.6o 40o/140o 36o/144o 32.7o/147.3o 6 5 7

12 sides 16 sides 20 sides Dodecagon Hexadecago n o 22.5o/157.5 Icosagon 30o/150o 18o/162o Diagrams not accurately drawn Exterior Angles of Polygons Calculate the value of the unknown angles. 2 1 88o x 125o 115o w Angle w = 360 (125 + 90) = 145o 3

80o 55 ? o 125o 65o y Angle y = 360 (90 + 55 + 80 + 65) 108o Angle x = 360 (108 + 88 + 115) = 49o 4 z 55o 45o 58o 122 ? o 70o 32o Angle z = 360 (32 + 70 + 55 + 45 + 122) Diagrams not accurately drawn Exterior Angles of Polygons Now try these ones by yourself. 1 2 110o

110o x w 85o 130o Angle w = 360 (130 + 90) = 140o 3 63o y Angle x = 360 (110 + 85 + 110) = 55o 4 115 o 73o Angle y = 360 (65 + 73 + 90 + 63) z 45o 55o 33o 130o 58o Angle z = 360 (33 + 58 + 50 + 55 + 45) Whats happened? (mathematically speaking) And finally:

A hendecagon is laying eggsagons! Thanks E.G (mathematical pie) Exterior Angles of Polygons worksheet Exterior Angles of Polygons Calculate the exterior and interior angles of each of these regular polygons. 2 1 3 7 sides 9 sides 4 10 sides to 1 dp 11 sides to 1 dp 6 5 12 sides 7 16 sides 20 sides Diagrams not

accurately drawn Exterior Angles of Polygons Calculate the value of the unknown angles. 2 1 88o x 125o 115o w 3 108o 80o 4 125o 65o 55o 45o 58o y z 70o 32o Diagrams not

accurately drawn Exterior Angles of Polygons Now try these ones by yourself. 1 2 110o 110o x w 85o 130o 3 63o y 4 115 o 73o z 45o 55o 33o 130o 58o

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