AMC 12 2011b Problem 10

Rectangle $ABCD$ has $AB=6$ and $BC=3$. Point $M$ is chosen on side $AB$ so that $\angle AMD=\angle CMD$. What is the degree measure of $\angle AMD$?

\textbf{(A)}\ 15 \textbf{(B)}\ 30 \textbf{(C)}\ 45 \textbf{(D)}\ 60 \textbf{(E)}\ 75