Chapter 5.2, Problem 8PSA

To determine

To Find: The lines which are parallel.

Answer to Problem 8PSA

  $\overleftrightarrow{RA}\parallel \overleftrightarrow{TP}\text{with }\overleftrightarrow{AP}\text{as transversal}\text{.}$

Explanation of Solution

Given:

  

Concept Used:

When parallel lines is intersected by a transversal angles, interior angles on the same side of transversal are supplementary.

Calculation:

Here, we have $m\angle A=\left(180-x\right)°\text{ and }m\angle P=x°$ , where $\angle A\text{and }\angle P\text{ are angles on the same side of transversal}$

  $\because \left(180-x\right)°+x°=180°$

  $\angle A\text{and }\angle P\text{ are supplementary angles}$

Since, when parallel lines is intersected by a transversal angles, interior angles on the same side of transversal are supplementary.

Thus, $\overleftrightarrow{RA}\parallel \overleftrightarrow{TP}\text{with }\overleftrightarrow{AP}\text{as transversal}\text{.}$