AHSME 1979 Problem 12

In the adjoining figure, $CD$ is the diameter of a semi-circle with center $O$. Point $A$ lies on the extension of $DC$ past $C$; point $E$ lies on the semi-circle, and $B$ is the point of intersection (distinct from $E$ ) of line segment $AE$ with the semi-circle. If length $AB$ equals length $OD$, and the measure of $\measuredangle EOD$ is $45^\circ$, then the measure of $\measuredangle BAO$ is $\textbf{(A) }10^\circ \textbf{(B) }15^\circ \textbf{(C) }20^\circ \textbf{(D) }25^\circ \textbf{(E) }30^\circ$