Angle XBY in Right Triangle

A triangle $ABC$ has a right angle at $B$ and $\angle A = a^\circ$. Point $X$ lies on $AC$ such that $AX = AB$. Point $Y$ lies on $AC$ such that $CY = CB$.

Prove that $\angle XBY$ has the same size independently of the other angles of the triangle and find the size of that angle.