2. 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.

3. Exterior Angles of Polygons Regular Polygons Square 4 Pentagon 5 Hexagon 6 Octagon 8 Equilateral Triangle 3 120 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

4. 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. 1 24 5 67 3 to 1 dp

5. Angle w = 360 – (125 + 90) = 145 o 1 2 3 4 88 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 – (108 + 88 + 115) = 49 o Angle y = 360 – (90 + 55 + 80 + 65) = 70 o Angle z = 360 – ( 32 + 70 + 55 + 45 + 122 ) = 36 o 122 o ? 55 o ?

6. Exterior Angles of Polygons Diagrams not accurately drawn Now try these ones by yourself. 3 4 63 o 73 o y 115 o 58 o z 33 o 55 o 130 o 45 o 12 110 o w 85 o 110 o x 130 o Angle w = 360 – (130 + 90) = 140 o Angle x = 360 – (110 + 85 + 110) = 55 o Angle y = 360 – (65 + 73 + 90 + 63) = 69 o Angle z = 360 – ( 33 + 58 + 50 + 55 + 45 ) = 119 o

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

8. Exterior Angles of Polygons worksheet

9. Calculate the exterior and interior angles of each of these regular polygons. 1 24 5 67 3 Exterior Angles of Polygons 7 sides10 sides11 sides 12 sides 16 sides20 sides 9 sides to 1 dp

10. 1 2 3 4 88 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

11. Exterior Angles of Polygons Diagrams not accurately drawn Now try these ones by yourself. 3 4 63 o 73 o y 115 o 58 o z 33 o 55 o 130 o 45 o 12 110 o w 85 o 110 o x 130 o