Chapter 5.2, Problem 18PSA

To determine

To Find: Whether $p\parallel q$ , with explanation.

Answer to Problem 18PSA

Yes, $p\parallel q$

Explanation of Solution

Given:

  

  $x=14.5$

Concept Used:

When two lines are parallel interior angles on the same side of transversal are supplementary.

Calculation:

As we have $x=14.5$ , thus

  $\begin{array}{l}\left(8x\right)°=\left(8\times 14.5\right)°=116°\left(1\right)\\ \left(5x-8.5\right)°=\left(5\times 14.5-8.5\right)°=\left(72.5-8.5\right)°=64°\left(2\right)\\ \text{Now,}\\ 116°+64°=180°\\ \Rightarrow \left(8x\right)°+\left(5x-8.5\right)°=180°=\left(\text{For }x=14.5\right)\\ \left(8x\right)°\text{ and }\left(5x-8.5\right)°\text{are supplementary angles}\text{.}\\ \text{Since, we know that when two lines are parallel, interior angles on the same side}\\ \text{of transversal are supplementary}\text{.}\\ \Rightarrow p\parallel q\end{array}$