Answer :
Angle 4 and 5 are alternate interior angles. Therefore, as the horizontal lines are parallel, they will have the same measure.
Then, we can write:
[tex]\begin{gathered} m\angle4=m\angle5 \\ 4x-17=5x-29 \\ 4x-5x=-29+17 \\ -x=-12 \\ x=12 \end{gathered}[/tex]Answer: In order for the angle to have the same measure, then the value for x is x=12.
NOTE: angle 4 is vertical angle with angle 1, which is corresponding to angle 5. Thats why 4 and 5 have the same measure.