MathNet 2015-part-01 — 191 problems (EN–VI) Question 180

A hexagon is called equiangular when all six of its interior angles are equal. Consider the equiangular hexagon $A B C D E F$ with sides $3, y, 5, 4, 1$ and $x$, shown in the following figure. Determine the unknown lengths $x$ and $y$.