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polygons

polygons. Definition: A polygon is a closed figure formed by a finite number of sides . 4. 6. 7. 5. 3. hexagon. triangle. quadrilateral. pentagon. heptagon. 8. 11. 9. 10. 12. hendecagon. octagon. nonagon. decagon. dodecagon. polygons.

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polygons

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  1. polygons Definition: A polygon is a closed figure formed by a finite number of sides. 4 6 7 5 3 Polygons - C. Harun Boke hexagon triangle quadrilateral pentagon heptagon 8 11 9 10 12 hendecagon octagon nonagon decagon dodecagon

  2. polygons Definition: A polygon that has equal sides and equal angles is called a regular polygon. Polygons - C. Harun Boke a regular quadrilateral (square) a regular heptagon (7-gon)

  3. polygons Interior and Exterior Angles of a Polygon: Angles inside a polygon are called interior angles, whereas Angles outside a polygon are called exterior angles. Polygons - C. Harun Boke

  4. polygons Sum of Interior Angles of a Polygon sum of interior angles of a triangle = 180° Polygons - C. Harun Boke

  5. polygons Sum of interior angles of a quadrilateral ? = 360° 180° 180° Polygons - C. Harun Boke 2 triangles = 2 x 180° = 360°

  6. polygons ? Sum of interior angles of a pentagon 180° = 540° 180° 180° Polygons - C. Harun Boke 3 triangles = 3 x 180° = 540°

  7. polygons Triangle => 3 sides => 1 triangle => 180° Quadrilateral => 4 sides => 2 triangles => 2 x 180° = 360° Pentagon => 5 sides => 3 triangles => 3 x 180° = 540° n-gon => n sides => n - 2 triangles => (n – 2) x 180° Polygons - C. Harun Boke Sum of interior angles of a polygon = (n – 2) x 180°

  8. polygons 10 sides => 10 angles (10 – 2) x 180 = 8 x 180 = 1440° 5 sides => 5 angles (5 – 2) x 180 = 3 x 180 = 540° Polygons - C. Harun Boke 8 sides => 8 angles (8 – 2) x 180 = 6 x 180 = 1080°

  9. polygons Sum of interior angles of pentagon = (n – 2) x 180 = (5 – 2) x 180 = 3 x 180 = 540° Polygons - C. Harun Boke 2x + 2x + (3x + 14) + (3x + 14) + 142 = 540 10x + 170 = 540 …… x = 37° <MHJ = <JKL = 2x = 2(37) = 74° <HML = <KLM = 3x + 14 = 3(37) + 14 = 125°

  10. polygons (4 – 2) x 180 = 2 x 180 = 360° x + 2x + 3x + 4x = 360° 10x = 360° x = 36° 2x = 2(36) = 72° 3x = 3(36) = 108° 4x = 4(36) = 144° (6 – 2) x 180 = 720° (x + 2) + (x– 4) + (x + 6) + (x – 3) + (x +7) + (x – 8) = 720° 6x = 720° x = 120° x +2 = 122°, x – 4 = 116°, x+ 6 = 126° x – 8 = 112°, x + 7 = 127°, x – 3 = 117° Polygons - C. Harun Boke

  11. polygons Finding the measure of each interior angle (n - 2) x 180 n = measure of each interior angle Polygons - C. Harun Boke = = = = 108 150 144 140 (5 – 2) x 180 5 (10 – 2) x 180 10 (12 – 2) x 180 12 (9 – 2) x 180 9

  12. polygons 360 Sum of Exterior Angles of Polygons = triangle quadrilateral pentagon hexagon Polygons - C. Harun Boke heptagon octagon nonagon decagon hendecagon dodecagon

  13. polygons 360 n One Exterior Angle of a Regular Polygon = n = 10 360 10 n = 5 360 5 Polygons - C. Harun Boke = 36 = 72 x – 11 + x + 10 + 31 + 2x – 42 = 360 4x – 12 = 360 …. x = 93 x – 11 = 93 – 11 = 82 x + 10 = 93 + 10 = 103 2x – 42 = 2(93) – 42 = 144

  14. polygons Finding the Number of Sides from the Measure of One Interior Angle Ex. Find the number of sides of a regular polygon with the measure of one interior angle 135°. 1st way 2nd way (n – 2) x 180 n One int. angle One ext. angle =135 + = 180 Polygons - C. Harun Boke (n – 2) x 180 = 135n 180n – 360 = 135n 180n – 135n = 360 45n = 360 n = 8 180 – 135 = 45 (one ext. angle) 360 n 45n = 360 n = 8 = 45

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