2014 AMC 8 Problems/Problem 9

Problem

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]$

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

Solution

$BD = DC$ , so $\angle DBC = \angle DCB = 70$ . Then $\angle CDB = 180-(70+70) = 40$ . Since $\angle ADB$ and $\angle BDC$ are supplementary, $\angle ADB = 180 - 40 = \boxed{\textbf{(D)}~140}$ .

2014 AMC 8 (Problems • Answer Key • Resources)
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2014 AMC 8 Problems/Problem 9

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