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In the diagram above, $A$ is on line segment $\overline{CE}$, and $\overline{AB}$ bisects $\angle DAC$ (meaning that $\overline{AB}$ splits $\angle DAC$ into two equal angles). If $\overline{DA}\parallel\overline{EF}$ and $\angle AEF = 10 \angle BAC - 12^\circ$, then what is $\angle DAC$ in degrees?

 Mar 3, 2020
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Let x = angle BAC.  Then angle BAD = x, and angle AEF = 10x - 12, so 2*2x = 180 - (10x - 12).  This leads to x = 96/7, so angle DAC = 96/7 degrees.

 Mar 3, 2020

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