2. The measure of two verticle angles are $58^{\circ}$ and $(3 x+4)^{\circ}$. Find the value of $x$.

Step 1 ：Given that the measure of two vertical angles are $58^{\circ}$ and $(3x+4)^{\circ}$, we know that the two vertical angles in a pair are always equal. Therefore, we can set up the equation $58 = 3x + 4$ and solve for $x$.

Step 2 ：Solving the equation gives us $x = 18$.

Step 3 ：Final Answer: The value of $x$ is \(\boxed{18}\).