Find the value of x for which ABCD must be a parallelogram.

The value of x is:
[tex]x=9[/tex]
We know that a parallelogram is a polygon with two pair of parallel sides which are congruent.
Based on the figure we get that side AD is congruent to side BC.
This means that:
[tex]x+26=4x-1[/tex]
on subtracting x from both the sides of the equation we have:
[tex]4x-x-1=26\\\\3x-1=26[/tex]
Now on adding 1 on both the sides of the equation we have:
[tex]3x=26+1\\\\3x=27\\\\x=\dfrac{27}{3}\\\\x=9[/tex]