1956 AHSME Problem 50

In \triangle ABC, \overline{CA} = \overline{CB}. On CB square BCDE is constructed away from the triangle. If x is the number of degrees in \angle DAB, then

\begin{array}{l} \textbf{(A)}\ x\text{ depends upon }\triangle ABC \qquad \textbf{(B)}\ x\text{ is independent of the triangle} \\ \textbf{(C)}\ x\text{ may equal }\angle CAD \qquad \\ \textbf{(D)}\ x\text{ can never equal }\angle CAB \\ \textbf{(E)}\ x\text{ is greater than }45^{\circ}\text{ but less than }90^{\circ} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.