ANSWER
[tex]x=21[/tex]
Option A
EXPLANATION
Recall, that the adjacent angles of a trapezoid add up to 180.
Hence;
[tex]\angle BAC+\angle DCA=180[/tex]
Given;
[tex]\begin{gathered} \angle BAC=3x+5 \\ \angle DCA=6x-4 \end{gathered}[/tex]
Now, let the sum of the angles be equal to 180.
[tex]3x-5+(6x-4)=180[/tex]
Solving by collecting like terms;
[tex]\begin{gathered} 3x-5+6x-4=180 \\ 3x+6x-5-4=180 \\ 9x-9=180 \\ 9x=180-9 \\ 9x=189 \end{gathered}[/tex]
Divide both sides by 9
[tex]\begin{gathered} 9x=189 \\ \frac{9x}{9}=\frac{189}{9} \\ x=21 \end{gathered}[/tex]
