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Exterior Angles of a Heptagon

Exterior Angles of a Heptagon
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2015-10-28 01:48
PolygonAngleTrigonometryGeometric Construction
In collections Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles Polygons & Angles
This GeoGebra example demonstrates the exterior angles of a heptagon (7-sided polygon) through rotation operations, providing a visual way to understand how exterior angles are formed. Key mathematical concepts include: (1) The theorem that the sum of exterior angles of any polygon equals 360°; (2) The relationship between exterior and interior angles; (3) Accumulation of rotation angles. Construction uses GeoGebra commands: Rotate to create exterior angles at each vertex, Polygon to construct the heptagon, Angle to measure angles, and Ray to draw exterior angle rays. Students can drag point A or use sliders to observe dynamic changes of exterior angles α, β, γ, etc., verifying that the sum always equals 360°. Suitable for middle school mathematics classes, teaching polygon angle properties, or as a geometric visualization resource.

GeoGebra Commands & Parameters

  1. Circle(A, 8 - a) → c
  2. Point(c) → B
  3. Line(A, B) → b
  4. Rotate(B, 51.7°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 51.7°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 51.7°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 51.7°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 51.7°, A) → C'
  13. Angle(C, A, C') → ε
  14. Rotate(C', 51.7°, A) → C''
  15. Angle(C', A, C'') → ζ
  16. CircleArc(A, B, B') → d
  17. CircleArc(A, B', B'') → e
  18. CircleArc(A, B'', B''') → f
  19. CircleArc(A, B''', C) → g
  20. CircleArc(A, C, C') → h
  21. CircleArc(A, C', C'') → k
  22. CircleArc(A, C'', B) → p
  23. Point(d) → D
  24. Point(e) → E
  25. Point(f) → F
  26. Point(g) → G
  27. Point(h) → H
  28. Point(k) → I
  29. Point(p) → J
  30. Ray(D, E) → i
  31. Ray(E, F) → j
  32. Ray(F, G) → l
  33. Ray(G, H) → m
  34. Ray(H, I) → n
  35. Ray(I, J) → q
  36. Ray(J, D) → r
  37. Circle(D, 1.5) → s
  38. Circle(E, 1.5) → t
  39. Circle(F, 1.5) → c_1
  40. Circle(G, 1.5) → d_1
  41. Circle(H, 1.5) → e_1
  42. Circle(I, 1.5) → f_1
  43. Circle(J, 1.5) → g_1
  44. Intersect(c_1, j, 2) → K
  45. Intersect(c_1, l, 1) → L
  46. Intersect(d_1, l, 2) → M
  47. Intersect(d_1, m, 1) → N
  48. Intersect(e_1, m, 2) → O
  49. Intersect(e_1, n, 1) → P
  50. Intersect(f_1, n, 2) → Q
  51. Intersect(f_1, q, 1) → R
  52. Intersect(g_1, q, 2) → S
  53. Intersect(g_1, r, 1) → T
  54. Intersect(s, r, 2) → U
  55. Intersect(s, i, 1) → V
  56. Intersect(t, j, 1) → W
  57. Intersect(t, i, 2) → Z
  58. CircleSector(F, K, L) → h_1
  59. CircleSector(G, M, N) → k_1
  60. CircleSector(H, O, P) → p_1
  61. CircleSector(I, Q, R) → q_1
  62. CircleSector(J, S, T) → r_1
  63. CircleSector(D, U, V) → s_1
  64. CircleSector(E, Z, W) → t_1
  65. Polygon(G, H, I, J, D, E, F) → poly1, g_2, h_2, i_1, j_1, d_2, e_2, f_2