Polygons with two different anglesI 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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Polygons with two different anglesI 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?

Jaylene Tyler · Accepted Answer

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              .

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?

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