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2013 AMC 12B Problems/Problem 13

Revision as of 15:56, 22 February 2013 by Zverevab (talk | contribs) (Created page with "==Problem== The internal angles of quadrilateral <math>ABCD</math> form an arithmetic progression. Triangles <math>ABD</math> and <math>DCB</math> are similar with <math>\angle ...")
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Problem

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 arithemetic progression. In degrees, what is the largest possible sum of the two largest angles of $ABCD$?

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

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