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Exterior angle of a convex polygon

Investigate the sum of the exterior angles of a polygon by clicking and dragging any of the blue points.

  1. What observation can you make regarding the sum of the exterior angles of a polygon?
  2. What relationship exists between any exterior angle and its adjacent interior angle?
  3. In a polygon with n sides, the sum of all interior angles and their adjacent exterior angles is n x 180°. The interior angle sum of a polygon with n sides is equal to (n - 2) x 180°. Using these two results, confirm you answer to question (1).