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 360 o.

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

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. 4 o/128. 6 o 40 o/140 o 36 o/144 o 32. 7 o/147. 3 o 6 5 7 12 sides 16 sides 20 sides Dodecagon Hexadecagon Icosagon 30 o/150 o 22. 5 o/157. 5 o 18 o/162 o

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

Diagrams not accurately drawn Exterior Angles of Polygons Now try these ones by yourself. 1 2 110 o x w 85 o 130 o Angle w = 360 – (130 + 90) = 140 o 3 63 o y Angle x = 360 – (110 + 85 + 110) = 55 o 4 115 o 73 o Angle y = 360 – (65 + 73 + 90 + 63) = 69 o z 45 o 33 o 130 o 55 o 58 o Angle z = 360 – (33 + 58 + 50 + 55 + 45) = 119 o

What’s 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 88 o x 125 o w 3 115 o 108 o 80 o 4 125 o 65 o y z 55 o 45 o 58 o 70 o 32 o

Diagrams not accurately drawn Exterior Angles of Polygons Now try these ones by yourself. 1 2 110 o x w 85 o 130 o 3 63 o y 4 115 o 73 o z 45 o 33 o 130 o 58 o 55 o