Plane geometry I · Chapter I · Consolidate
Let \(ABCDE\) be a convex pentagon whose five sides all have the same length. Suppose that two of its diagonals meet at an angle of \(60^\circ\). Prove that the pentagon has two parallel sides.
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Serbian Municipal Competition 2016, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source