Chapter 12.2, Problem 18E

To determine

To find: the value of $x$ that makes lines $m$ and $n$ parallel.

Answer to Problem 18E

The value of $x=\frac{62}{3}$ that makes lines $m$ and $n$ parallel.

Explanation of Solution

Given information : Angle ${58}^{\circ }$ and ${(3x-4)}^{\circ }$ are corresponding angles.

Concept used : Pair of angles that are at the same position at each intersection on the same side of the transversal known as corresponding angles. Here, ${58}^{\circ }$ and ${(3x-4)}^{\circ }$ are corresponding angles and we know that the value of corresponding are always equal.

Calculation :

  $\begin{array}{l}$ {(3x-4)}^{\circ }={58}^{\circ }$\Rightarrow 3x=58+4\\ \Rightarrow 3x=62\\ \Rightarrow x=\frac{62}{3}\end{array}$

So, the value of $x=\frac{62}{3}$