Exterior Angles of Polygons

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Presentation transcript:

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

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

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

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

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

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. 1 2 4 5 6 7 3 Exterior Angles of Polygons 7 sides 10 sides 11 sides 12 sides 16 sides 20 sides 9 sides to 1 dp

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

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