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pairs of equal angles in hexagon, if AB =CD=EF, BC=DE=FA , <A+<B =<C <D=<E+<F

Source: 2016 Saudi Arabia IMO TST , level 4+, IV p2

July 27, 2020
convexhexagonequal segmentsanglesequal anglesgeometry

Problem Statement

Let ABCDEFABCDEF be a convex hexagon with AB=CD=EFAB = CD = EF, BC=DE=FABC =DE = FA and ∠A+∠B=∠C+∠D=∠E+∠F\angle A+\angle B = \angle C +\angle D = \angle E +\angle F. Prove that ∠A=∠C=∠E\angle A=\angle C=\angle E and ∠B=∠D=∠F\angle B=\angle D=\angle F.
Tran Quang Hung
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