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convex pentagon with each diagonal an angle trisector, is it regular?

Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 1, p3

April 10, 2020
pentagongeometryconvexdiagonalstrisectordiagonal

Problem Statement

The diagonals of a convex pentagon divide each of its interior angles into three equal parts. Does it follow that the pentagon is regular?