geometry

Question

geometry

0

271

2

As shown in the diagram $\angle BAC=90^\circ$ . Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$ , $\overline{AY}$ be the bisector of $\angle BAC$ , and $\overline{AZ}$ be the median of $\triangle ABC$ . If $\angle XAY = 18^\circ$ , then what is the measure of $\angle ZAC$ in degrees?

[asy] size(7cm);pair A,B,C, X,Y,Z;B = (-1,0);C = (1,0);A = rotate(116)*(1,0);X = foot(A,B,C);Z = (0,0);Y = intersectionpoint(A--(bisectorpoint(B,A,C)), B--C);draw(Y--A--C--B--A--Z);draw(X--A);draw(rightanglemark(B,A,C,2.5));draw(rightanglemark(A,X,B,2.5));label(