Question

Find the value of $x$ that makes lines $m$ and $v$ parallel.

Short answer

The value of $x$ is $x=\frac{62}{3}$.

Step-by-step solution

Step 1. Given Information.

The provided figure is

Two angles are provided having measures $58°$ and $\left(3x-4\right)°$.

Step 2. Definition of corresponding angles.

When two lines are crossed by another line, it is known as transversal.

Corresponding angles are angles that are at the same relative position at each intersection. The measure of two corresponding angles is equal.

Step 3. Calculation.

From the given diagram, angle $58°$ and $\left(3x-4\right)°$ are corresponding angles. So, both the angles must be equal, that is, $\left(3x-4\right){}^{\circ }=58°$.

The value of $x$ is,

$\begin{array}{c}\left(3x-4\right)°=58°\\ 3x=58+4\\ 3x=62\\ x=\frac{62}{3}\end{array}$

Step 4. Conclusion.

The value$x$ of is $x=\frac{62}{3}$.