AMC 12 2013b Problem 13

The internal angles of quadrilateral $ABCD$ form an arithmetic progression. Triangles $ABD$ and $DCB$ are similar with $\angle DBA = \angle DCB$ and $\angle ADB = \angle CBD$. Moreover, the angles in each of these two triangles also form an arithmetic progression. In degrees, what is the largest possible sum of the two largest angles of $ABCD$?

\textbf{(A)}\ 210 \textbf{(B)}\ 220 \textbf{(C)}\ 230 \textbf{(D)}\ 240 \textbf{(E)}\ 250