Difference between revisions of "2014 AMC 8 Problems/Problem 9"

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<math> \textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad\textbf{(E) }150 </math>
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In <math>\bigtriangleup ABC</math>, <math>D</math> is a point on side <math>\overline{AC}</math> such that <math>BD=DC</math> and <math>\angle BCD</math> measures <math>70^\circ</math>. What is the degree measure of <math>\angle ADB</math>?
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[asy]
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size(300);
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defaultpen(linewidth(0.8));
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pair A=(-1,0),C=(1,0),B=dir(40),D=origin;
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draw(A--B--C--A);
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draw(D--B);
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dot("<math>A</math>", A, SW);
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dot("<math>B</math>", B, NE);
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dot("<math>C</math>", C, SE);
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dot("<math>D</math>", D, S);
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label("<math>70^\circ</math>",C,2*dir(180-35));[/asy]
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<math>\textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad \textbf{(E) }150</math>

Revision as of 19:16, 26 November 2014

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]

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