2011 AMC 10B Problem 18

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

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