Exterior Angles of a Regular Polygon
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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
Circle(A, n) → cPoint(c) → BPolygon(A, B, 9) → poly1, a, C, D, E, F, G, H, I, b, d, e, f, g, h, i, jRay(A, B) → kRay(B, C) → lRay(C, D) → mRay(D, E) → pRay(E, F) → qRay(F, G) → rRay(G, H) → sRay(H, I) → tRay(I, A) → a_1Angle(l, m) → αAngle(m, e) → βAngle(p, q) → γAngle(q, r) → δAngle(r, s) → εAngle(s, t) → ζAngle(t, a_1) → ηAngle(a_1, k) → θAngle(k, l) → ι