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<A=<D, <B=<E, <C=<F if ABCDEF is convex 6-gon, <A+<C+<E=<B+<D+<F, equal sides

Source: 1953 Hungary - Kürschák Competition p3

October 10, 2022
geometryequal segmentsequal angleshexagon

Problem Statement

ABCDEFABCDEF is a convex hexagon with all its sides equal. Also ∠A+∠C+∠E=∠B+∠D+∠F\angle A + \angle C + \angle E = \angle B + \angle D + \angle F. Show that ∠A=∠D\angle A = \angle D, ∠B=∠E\angle B = \angle E and ∠C=∠F\angle C = \angle F.
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