[tex]m\angle2+m\angle3=180^0(Adjacent\text{ sides of a parallelogram are supplementary)}[/tex][tex]m\angle2=m\angle4\text{ (opposite angles of a parrallelogram are equal)}[/tex]
We going to use the second condition to obtain the value of x first, then go back to the first condition to obtain the required measure of angle 3.
Thus, we have:
[tex]\begin{gathered} m\angle2=m\angle4 \\ 4x-22=3x-6 \\ 4x-3x=-6+22 \\ x=16^0 \end{gathered}[/tex]
Having gotten the value of x, then we can now find the required measure of angle 3.
Thus, we have:
[tex]\begin{gathered} m\angle2+m\angle3=180^0^{} \\ 4x-22+m\angle3=180 \\ m\angle3=180-4x+22 \\ x\text{ has b}een\text{ to be 16} \\ m\angle3=180-4(16)+22 \\ m\angle3=180-64+22 \\ m\angle3=138^0 \end{gathered}[/tex]
Hence, the correct option is option A
