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Shape and Space

Shape and Space. EXTERNAL ANGLES. EXTERNAL ANGLES. The external angle is the angle that the arrow needs to turn when changing direction from AB to BC. C. B. A. SQUARE. The four angles create 360 ° 360 ÷ 4 = 90° One external angle is 90°. REGULAR PENTAGON.

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Shape and Space

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  1. Shape and Space EXTERNAL ANGLES

  2. EXTERNAL ANGLES • The external angle is the angle that the • arrow needs to turn when changing • direction from AB to BC. C B A

  3. SQUARE The four angles create 360° 360 ÷ 4 = 90° One external angle is 90°

  4. REGULAR PENTAGON The five angles create 360° 360 ÷ 5 = 72° One external angle is 72°

  5. REGULAR HEXAGON The six angles create 360° 360 ÷ 6 = 60° One external angle is 60°

  6. EXERCISES • 1. Calculate the external angle of a regular heptagon (7 sides). • 2. Calculate the external angle of a regular octagon (8 sides). • 3. Calculate the external angle of a regular nonagon (9 sides). • 4. Calculate the external angle of a regular decagon (10 sides). • 5. Calculate the external angle of a regular hendecagon (11 sides). • 6. Calculate the external angle of a regular dodecagon (12 sides). • What does the external angle tend to when the number of sides increase?

  7. IRREGULAR POLYGON • The sum of external angles of a polygon always adds to 360° 73° 73° 65° 65° 59° 22° + 219° 59° 360° A _ 219° 22° 141° A = 141°

  8. IRREGULAR POLYGON • The sum of external angles of a polygon always adds to 360° 88° 45° 45° 38° 88° 38° 43° 25° + 239° 43° 360° _ 239° 25° B 121° B = 121°

  9. EXERCISES • Calculate the angles marked with letters 80° 66° 75° 100° 98° 91° B A 95° C 90° 85° 57° 25° 33°

  10. EXTERNAL + INTERNAL = 180° • Adding the external and • internal angles together • always gives a total of 180° • This is true for regular • and irregular polygons

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