In the diagram below, A is on line segment CE and AB bisects Angle DAC. If segment DA is parallel to segment EF and angle AEF = 10angleBAC - \(22\) degrees, then what is angle DAC in degrees?
+14917 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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+1622 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.
