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Brainteasers

The angles of a twenty-sided polygon

geometrypolygonsangles

A convex polygon has 20 sides.

  1. What is the sum of its interior angles?
  2. If it is regular, what is each interior angle, and each exterior angle?
  3. Explain both results with a picture rather than a memorised formula.
Show a hint

Cut the polygon into triangles from one corner. Or walk around the boundary and count how far you turn in total.

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