Track / Stage 4 / 61 of 340 #321 of 2000

31. In a convex pentagon $A B C D E$, all sides are equal, and the angle $A C E$ is half the angle $B C D$. Find the angle $A C E$.

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Official solution

76.31. Answer. $30^{\circ}$. Hint. Apply to the given pentagon a triangle $C D A^{\prime}$, equal to triangle $C B A$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.