Chapter 12.2, Problem 17E

To determine

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

Answer to Problem 17E

The value of $x=5$ that makes lines $m$ and $n$ parallel.

Explanation of Solution

Given information : Angle ${30}^{\circ }$ and $6x^{\circ }$ 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, ${30}^{\circ }$ and $6x^{\circ }$ are corresponding angles and we know that the value of corresponding are always equal.

Calculation :

  $\begin{array}{l}6x^{\circ }={30}^{\circ }\\ \Rightarrow x=\frac{30}{6}\\ \Rightarrow x=5\end{array}$

So, the value of $x=5$ .