# Geometry Problem 1499: Triangle Angles, Cevian, Congruence, Isosceles and Equilateral Triangles, and Auxiliary Construction

In triangle ABC,
point E lies on
\({\overline {AC}}\) such that \({\angle{BCA}}={2x},{\angle{BEA}}={3x},{\angle{A}}={60^\circ-2x}\)
and AE = BC.
Find the value of \({x}\).

Auxiliary
construction is an extra line, point or circle needed to complete a proof
or solution in geometry.

View solution

## Typography and Sketch for Problem 1498: Chichen Itza in the Background

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