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In the diagram below, $A$ 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? [asy] pair A,B,C,D,EE,F; A = (0,0); B = rotate(164)*(1,0); C = rotate(148)*(1,0); D = (-1,0); EE = -0.4*C; F = EE + (1,0); dot(B,p=black+3bp); dot(C,p=black+3bp); dot(D,p=black+3bp); dot(F,p=black+3bp); draw(F--EE--C); draw(B--A--D); label("$B$",B,NW); label("$A$",A,NE); label("$C$",C,N); label("$D$",D,W); label("$E$",EE,S); label("$F$",F,E); [/asy]

 Mar 16, 2020
 #1
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Anyone who tried to makes sense of that would also be sleep deprived.

 Mar 16, 2020

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