Question 4
Let $ABC$ be a triangle with $\angle ABC = 2 \cdot \angle ACB$. Let $X$ and $Y$ be the midpoints of arcs $AB$ and $BC$ (not containing $C$ and $A$, respectively) of the circumcircle of triangle $ABC$. Let $BL$ be the angle bisector of $\angle ABC$, with $L \in AC$. Given that $\angle XLY = 90^\circ$, determine the measures of the angles of triangle $ABC$.