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 What is angle DAC in degrees?

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$AEF+BAC+BAD=180^o\\ 12BAC=180^o\\2BAC=\color{red}DAC=30^o\ error \\ $

$10BAC-22^o+DAC=180^o\\ 5DAC-22^o+DAC=180^o\\ 6DAC=202^o\\ \color{blue}DAC=33\frac{2}{3}^o$

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By alternate interior angles, angleAEF is congruent to angleDAE. 

Since CAE is a straight line, then it has a straight angle. Therefore angleBAC + angleBAD + angleDAE = 180degrees.

angleDAE = angleAEF = 10angleBAC - 22degrees.

Since angleBAC = angleBAD because BA is an angle bisector, then we can simplify the equation to:

angleBAC + angleBAC + 10angleBAC - 22 = 180degrees.

To simplify:

12 * angleBAC = 202degrees.

To simplify:

angleBAC = (101/6)degrees.

Since we are looking for angleDAC, and we also know 2 * angleBAC = angleDAC, then angleDAC = $101\over3$degrees.

∠BAC = x              ∠DAC = 2x

2x + 10x - 22 = 180