# 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 $B$.