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Interior Angles of Polygons

Interior Angles of Polygons. 5 sides. 4 sides. 3. 4 x 180 o = 720 o. 3 x 180 o = 540 o. 2 x 180 o = 360 o. 2. 180 o. 6 sides. 7 sides. 5 x 180 o = 900 o. 4. 5. (n – 2) triangles = (n – 2)180 o.

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Interior Angles of Polygons

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  1. Interior Angles of Polygons 5 sides 4 sides 3 4 x 180o = 720o 3 x 180o = 540o 2 x 180o = 360o 2 180o 6 sides 7 sides 5 x 180o = 900o 4 5 (n – 2) triangles = (n – 2)180o Find the connection between the number of sides and the number of triangles. 180o 180o 180o 180o 180o Pentagon Quadrilateral The sum of the interior angles of an” n” sided polygon is? 180o 180o 180o 180o 180o 180o 180o 180o Heptagon/Septagon Hexagon

  2. Calculate the angle sum and interior angle of each of these regular polygons. 2 3 4 1 7 sides 10 sides 11 sides 9 sides 6 7 5 12 sides 16 sides 20 sides Interior Angles of Polygons to 1 dp to 1 dp Nonagon Septagon/Heptagon Decagon Hendecagon 1260o/140o 900o/128.6o 1440o /144o 1620o /147.3o Hexadecagon Icosagon Dodecagon 2520o /157.5o 3240o /162o 1800o /150o

  3. Find the unknown angles below. x Diagrams not drawn accurately. 100o 75o 95o w 115o 110o 75o 70o 125o 125o z 100o 140o 138o 105o 121o 138o 117o y 133o 137o Interior Angles of Polygons 3 x 180o = 540o 2 x 180o = 360o 540 – 395 = 145o 360 – 245 = 115o 4 x 180o = 720o 5 x 180o = 900o 720 – 603 = 117o 900 – 776 = 124o

  4. Now try these ones yourself. 115o 120o 2 1 115o 88o 95o y 120o 85o x 120o 155o 3 x 180o = 540o Diagrams not drawn accurately. 4 x 180o = 720o 540 – 418 = 122o 720 – 595 = 125o 165o 3 4 125o w 150o 95o 75o 75o 155o z 2 x 180o = 360o 5 x 180o = 900o 360 – 240 = 120o 900 – 780 = 120o Interior Angles of Polygons

  5. Interior Angles of Polygons

  6. Interior Angles of Polygons Calculate the angle sum and interior angle of each of these regular polygons. 2 3 4 1 7 sides 10 sides 11 sides 9 sides to 1 dp to 1 dp 6 7 5 12 sides 16 sides 20 sides

  7. Interior Angles of Polygons Find the unknown angles below. x Diagrams not drawn accurately. 100o 75o 95o w 115o 110o 75o 70o 125o 125o z 100o 140o 138o 105o 121o 138o 117o y 133o 137o

  8. Interior Angles of Polygons Now try these ones yourself. 115o 120o 2 1 115o 88o 95o y 120o 85o x 120o 155o Diagrams not drawn accurately. 165o 3 4 125o w 150o 95o 75o 75o 155o z

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

  10. 72o 90o 108o 120o 72o 90o 90o 90o 60o 108o 108o Square Pentagon 72o 3 4 5 108o 72o 120o 108o 90o 90o 90o 60o 60o 120o 90o 72o Equilateral Triangle 45o 60o 45o 45o 60o 60o Octagon Hexagon 45o 45o 6 8 60o 60o 45o 45o 60o 45o Exterior Angles of Polygons Regular Polygons Interior angles are 180 – 45 = 135o Interior angles are 180 – 60 = 120o

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

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

  13. 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 Angle x = 360 – (110 + 85 + 110) = 55o z y 4 63o 3 45o 55o 33o 115o 130o 58o 73o Angle z = 360 – (33 + 58 + 50 + 55 + 45) = 119o Angle y = 360 – (65 + 73 + 90+ 63) = 69o

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

  15. Exterior Angles of Polygons worksheet

  16. Exterior Angles of Polygons Calculate the exterior and interior angles of each of these regular polygons. 2 3 4 1 7 sides 10 sides 11 sides 9 sides to 1 dp to 1 dp 6 7 5 12 sides 16 sides 20 sides

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

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

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