Because the two labelled line segments are parallel, it follows that the two triangles are similar and corresponding sides occur in the same ratio with one another.
In particular, this means
[tex]\dfrac{2x-5}{(2x-5)+(x+8)}=\dfrac{22.5}{22.5+20}[/tex]
Solve for [tex]x[/tex]:
[tex]\dfrac{2x-5}{3x+3}=\dfrac{22.5}{42.5}[/tex]
[tex]\implies42.5(2x-5)=22.5(3x+3)[/tex]
[tex]\implies85x-212.5=67.5x+67.5[/tex]
[tex]\implies17.5x=280[/tex]
[tex]\implies\boxed{x=16}[/tex]
