In the given figure, we have two angles ADB and CDD which are vertical angles.
Vertical angles are also called opposite angles since they are opposite to each other.
Recall that vertical angles are always equal.
So that means we can equate these two angles
[tex]3x+30=5x+16[/tex]Now we can easily solve this equation for x.
[tex]\begin{gathered} 3x+30=5x+16 \\ 3x-5x=16-30 \\ -2x=-14 \\ 2x=14 \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex]Therefore, the value of x is 7.