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Use your protractor to measure the exterior angles of these shapes. Make a statement about your findings. Exterior Angles of Polygons Interior Angles Exterior Angles ? 180 o Exterior angles of a polygon sum to 360 o.

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

Exterior Angles of Polygons Septagon/HeptagonDecagonHendecagon Dodecagon Hexadecagon Icosagon 7 sides10 sides11 sides 12 sides 16 sides20 sides 9 sides Nonagon 51.4 o /128.6 o 40 o /140 o 36 o /144 o 32.7 o /147.3 o 30 o /150 o 22.5 o /157.5 o 18 o /162 o Calculate the exterior and interior angles of each of these regular polygons to 1 dp

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

Exterior Angles of Polygons Diagrams not accurately drawn Now try these ones by yourself o 73 o y 115 o 58 o z 33 o 55 o 130 o 45 o o w 85 o 110 o x 130 o Angle w = 360 – ( ) = 140 o Angle x = 360 – ( ) = 55 o Angle y = 360 – ( ) = 69 o Angle z = 360 – ( ) = 119 o

What’s happened? (mathematically speaking) A hendecagon is laying eggsagons! Thanks E.G (mathematical pie) And finally:

Exterior Angles of Polygons worksheet

Calculate the exterior and interior angles of each of these regular polygons Exterior Angles of Polygons 7 sides10 sides11 sides 12 sides 16 sides20 sides 9 sides to 1 dp

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

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