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POLYGONS

POLYGONS. A polygon is a shape enclosed by straight lines. TRIANGLE. QUADRILATERAL. sum of interior angles . sum of interior angles = 180°. = 2 x 180 ° = 360 °. PENTAGON. HEXAGON. sum of interior angles . sum of interior angles . = 4 x 180 ° = 720 °. = 3 x 180 ° = 540 °.

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POLYGONS

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  1. POLYGONS

  2. A polygon is a shape enclosed by straight lines.

  3. TRIANGLE QUADRILATERAL sum of interior angles sum of interior angles = 180° = 2 x 180° = 360° PENTAGON HEXAGON sum of interior angles sum of interior angles = 4 x 180° = 720° = 3 x 180°= 540°

  4. An n-sided polygon can be split into (n– 2) triangles. The sum of the interior angles in an n-sided polygon = (n– 2) x 180° Example Find the sum of the interior angles in a nonagon. Sum of interior angles = (n– 2) x 180° = (9 – 2) x 180° = 7 x 180° = 1260°

  5. x 140° 107° 75° 105° Example Find the value of x. Sum of interior angles = (5 – 2) x 180° = 540° x + 75 + 105 + 107 + 140 = 540 x + 427 = 540 x = 113°

  6. In a regular polygon • All the sides are the same length AND • All the angles are the same size

  7. Regular or not?        

  8. EXTERIORANGLE INTERIORANGLE

  9. Regular hexagon Sum of exterior angles = 360° 60° 120° Exterior angle = 360° ÷ 6 = 60° Interior angle = 180° – 60° = 120°

  10. Regular pentagon Sum of exterior angles = 360° 108° 72° Exterior angle = 360° ÷ 5 = 7° Interior angle = 180° – 72° = 108°

  11. Regular octagon Sum of exterior angles = 360° 45° 135° Exterior angle = 360° ÷ 8 = 45° Interior angle = 180° – 45° = 135°

  12. Exterior angle = Interior angle = In a regular n-sided polygon: Example The interior angle of a regular polygon is 156°. How many sides does the polygon have? Interior angle = The polygon has 15 sides.

  13. F E D x C A B Example ABCDE is a regular pentagon. Find the size of angle x . 72° 72° Angle AEF = exterior angle = 360 ÷ 5 = 72° Angle EAF = 72° x = 180 – (72 + 72) = 36°

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