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Sum of Exterior Angles of a Regular Polygon by Aarnout Brombacher

Sum of Exterior Angles of a Regular Polygon by Aarnout Brombacher
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2020-06-28 21:36
PolygonAngleGeometric Construction
This example demonstrates the constant sum of exterior angles for any regular polygon. Key math concepts include exterior angles, polygons, and angle measurement. It is constructed using GeoGebra commands like Circle, Intersect, Rotate, Angle, Ray, Polygon, and Segment to form the polygon and calculate its exterior angles, making it suitable for middle school and high school students learning about polygon properties and spatial geometry.

GeoGebra Commands & Parameters

  1. Circle(A, r) → c
  2. Intersect(c, xAxis, 2) → B
  3. Circle(A, 6) → d
  4. Rotate(B, (360°) / n, A) → B'
  5. Angle(B, A, B') → α
  6. Ray(B, B') → f
  7. Polygon(B, B', n) → poly1, g, s, C, D, E, F, G, H, I, J, h, i, j, k, l, m, p, q
  8. Ray(B', C) → t
  9. Ray(C, D) → a
  10. Ray(D, E) → b
  11. Ray(E, F) → e
  12. Ray(F, G) → f_1
  13. Ray(G, H) → g_1
  14. Ray(H, I) → h_1
  15. Ray(I, J) → i_1
  16. Ray(J, B) → j_1
  17. Intersect(d, j_1) → K,
  18. Intersect(d, f) → L,
  19. Intersect(d, t) → M,
  20. Intersect(d, a) → N,
  21. Intersect(d, b) → O,
  22. Intersect(d, e) → P,
  23. Intersect(d, f_1) → Q,
  24. Intersect(d, g_1) → R,
  25. Intersect(d, h_1) → S,
  26. Intersect(d, i_1) → T,
  27. Segment(B', M) → k_1
  28. Segment(C, N) → l_1
  29. Segment(D, O) → m_1
  30. Segment(E, P) → n_1
  31. Segment(F, Q) → p_1
  32. Segment(G, R) → q_1
  33. Segment(H, S) → r_1
  34. Segment(B, L) → s_1
  35. Segment(I, T) → t_1
  36. Rotate(B, (-((360°) / n)), A) → B'_1
  37. Rotate(L, (-((360°) / n)), A) → L'
  38. Segment(B'_1, L') → a_1
  39. Angle(L, B', M) → β
  40. Angle(M, C, N) → γ
  41. Angle(N, D, O) → δ
  42. Angle(O, E, P) → ε
  43. Angle(P, F, Q) → ζ
  44. Angle(Q, G, R) → η
  45. Angle(R, H, S) → θ
  46. Angle(S, I, T) → ι
  47. Angle(T, J, K) → λ
  48. Angle(L', B, L) → κ
  49. Rotate(B'_1, (-((360°) / n)), A) → U
  50. Rotate(L', (-((360°) / n)), A) → L''
  51. Segment(U, L'') → b_1
  52. Angle(L'', B'_1, L') → μ