Let ABC be a triangle where $\angle ABC = 90^\circ$. Draw point $Z$ on $AB$ such that $CB=CZ$, draw point $Y$ on $AC$ such that $CZ=YZ$, draw point $X$ such that $YZ=YX$, and draw point $W$ such that $YX=WX=AW$. Find $\angle A.$
Angle A = 30 degrees.
