Exterior Angles of a Regular Polygon

Exterior Angles of a Regular Polygon
Loading the math board and drawing, please wait…
2015-11-17 01:19
This example dynamically demonstrates the exterior‑angle property of regular polygons, showing each exterior angle and the constant sum of 360° for any number of sides. Core concepts include regular polygons, exterior angles, interior‑exterior angle relationships, and the polygon exterior‑angle sum theorem. Construction highlights: Circle creates the circumcircle, Point places vertices, Polygon builds the regular n‑gon, Ray draws exterior‑angle rays, Angle measures them, and a slider n controls the side count; objects such as n, A, c, B, poly1, a, b, d, e, f, g, h, i, j are used. Suitable for middle‑school geometry lessons, high‑school review, and independent exploration.

GeoGebra Commands & Parameters

  1. Circle(A, n) → c
  2. Point(c) → B
  3. Polygon(A, B, 9) → poly1, a, C, D, E, F, G, H, I, b, d, e, f, g, h, i, j
  4. Ray(A, B) → k
  5. Ray(B, C) → l
  6. Ray(C, D) → m
  7. Ray(D, E) → p
  8. Ray(E, F) → q
  9. Ray(F, G) → r
  10. Ray(G, H) → s
  11. Ray(H, I) → t
  12. Ray(I, A) → a_1
  13. Angle(l, m) → α
  14. Angle(m, e) → β
  15. Angle(p, q) → γ
  16. Angle(q, r) → δ
  17. Angle(r, s) → ε
  18. Angle(s, t) → ζ
  19. Angle(t, a_1) → η
  20. Angle(a_1, k) → θ
  21. Angle(k, l) → ι