2005 CEMC Gauss (Grade 7) Problems/Problem 8

Problem

In the diagram, what is the measure of $\angle ACB$ in degrees? $[asy] size(300); draw((-60,0)--(0,0)); draw((0,0)--(64.3,76.6)--(166,0)--cycle); label("$A$",(64.3,76.6),N); label("$93^\circ$",(64.3,73),S); label("$130^\circ$",(0,0),NW); label("$B$",(0,0),S); label("$D$",(-60,0),S); label("$C$",(166,0),S); [/asy]$

$\text{(A)}\ 57^\circ \qquad \text{(B)}\ 37^\circ \qquad \text{(C)}\ 47^\circ \qquad \text{(D)}\ 60^\circ \qquad \text{(E)}\ 17^\circ$

Solution

Since $\angle ABC + \angle ABD = 180^\circ$ (in other words, $\angle ABC$ and $\angle ABD$ are supplementary) and $\angle ABD = 130^\circ$ , then $\angle ABC = 50^\circ$ . Since the sum of the angles in triangle $ABC$ is $180^\circ$ and we know two angles $93^\circ$ and $50^\circ$ which add to $143^\circ$ , then $\angle ACB = 180^\circ - 143^\circ = 37^\circ$ . The answer is $B$ .

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2005 CEMC Gauss (Grade 7) Problems/Problem 8

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Solution

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