1. As shown in Figure 1, in $\triangle A B C$, $\angle A>90^{\circ}, D$ is a point on side $B C$ such that $A B$ is tangent to the circumcircle of $\triangle A C D$ at point $A$. The projection of point $B$ onto line $A D$ is $E$. If $C A=C D, A E=C E$, find the measure of $\angle B C A$.