2014 AMC 8 Problems/Problem 9

In $\bigtriangleup ABC$ , $D$ is a point on side $\overline{AC}$ such that $BD=DC$ and $\angle BCD$ measures $70^\circ$ . What is the degree measure of $\angle ADB$ ?

<asy> size(300); defaultpen(linewidth(0.8)); pair A=(-1,0),C=(1,0),B=dir(40),D=origin; draw(A--B--C--A); draw(D--B); dot(" $A$ ", A, SW); dot(" $B$ ", B, NE); dot(" $C$ ", C, SE); dot(" $D$ ", D, S); label(" $70^\circ$ ",C,2*dir(180-35));\<\asy>

$\textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad \textbf{(E) }150$

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2014 AMC 8 Problems/Problem 9