lines M and N shown below are parallel linesWhat is the valie of x in the measure of the angle?

These two angles are corresponding angles, if you link them with a line, it'll form an F shape, this means that they are congruent.
Since the angles are equal, you can say that
4x-20=84
Now you have a one unknown equation and can calculate the value of x:
[tex]\begin{gathered} 4x+20=84 \\ 4x=84+20 \\ 4x=104 \\ x=\frac{104}{4} \\ x=26 \end{gathered}[/tex]x=26º