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Exploring Interior Angles of Regular Polygons: Patterns and Conjectures

This exploration delves into the sum of interior angles of various regular polygons including equilateral triangles, squares, pentagons, hexagons, and more, analyzing their angle measures. Investigate the formulas used to calculate the sum of angles, specifically (n-2)·180°, and explore how these sums correlate with the number of sides in each polygon. Discover patterns among angles as the number of sides increases, culminating in an understanding of how geometry interrelates with polygon properties.

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Exploring Interior Angles of Regular Polygons: Patterns and Conjectures

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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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