2013 AMC 12B 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 \qquad \textbf{(B)}\ 220 \qquad \textbf{(C)}\ 230 \qquad \textbf{(D)}\ 240 \qquad \textbf{(E)}\ 250

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