A hexagon is called equiangular when it has six equal internal angles. Consider the equiangular hexagon $A B C D E F$ with sides $3, y, 5, 4, 1$, and $x$, as shown in the figure below. Determine the unknown lengths $x$ and $y$.

![](https://cdn.mathpix.com/cropped/2024_05_01_360f8ce7ec440aed2c7ag-35.jpg?height=446&width=462&top_left_y=925&top_left_x=891)