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5.1 Polygon Sum Conjecture

5.1 Polygon Sum Conjecture. Angle Exploration. Equilateral Triangle 60 °. Angle Exploration. Square 90 °. Angle Exploration. Regular Pentagon 108 °. Angle Exploration. Regular Hexagon 120 °. Angle Exploration. Regular Heptagon 129 °. Angle Exploration. Regular Octagon 135 °.

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5.1 Polygon Sum Conjecture

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  1. 5.1 Polygon Sum Conjecture

  2. Angle Exploration Equilateral Triangle 60°

  3. Angle Exploration Square 90°

  4. Angle Exploration Regular Pentagon 108°

  5. Angle Exploration Regular Hexagon 120°

  6. Angle Exploration Regular Heptagon 129°

  7. Angle Exploration Regular Octagon 135°

  8. Angle Exploration Regular Nonagon 140°

  9. Angle Exploration Regular Decagon 144°

  10. Angle Exploration Regular Dodecagon 147°

  11. Angle Exploration • Summarize our results Is there a correlation between the number of sides and the degrees?

  12. Angle Exploration • What is the sum of the angles in each of the polygons

  13. Angle Exploration • Summarize our results Total Degrees in each polygon. Do you see a pattern?

  14. Interior Angles in a Polygon • The sum of the angles of the interior angles of a convex n-gon is (n-2)•180°

  15. Interior Angles in a Polygon • What are the angle measures if the polygon is regular • (n-2)•180°/n

  16. Sample Problems

  17. X=96

  18. X=85

  19. X=97

  20. X=117

  21. Exercise 12

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