Let us consider polygons with only two different interior angles alpha and beta=pi-alpha. For which frequencies of these angles is it possible to form a closed polygon?

Brenton Dixon 2022-07-16 Answered
Polygons with two different angles
I have the following questions:
Let us consider polygons with only two different interior angles α and β = π α.
For which frequencies of these angles is it possible to form a closed polygon?
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Answers (1)

Jaylene Tyler
Answered 2022-07-17 Author has 10 answers
Explanation:
If the interior angles of a simple polygon are α 1 , , α n , then ( π α i ) = 2 π. Here we have k 1 times α and k 2 times β, so need k 1 ( π α ) + k 2 ( π β ) = 2 π, or k 1 π + ( k 2 k 1 ) α = 2 π, which amounts to either k 1 = k 2 = 2 or α = ( k 1 2 ) π k 1 k 2 .

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