Question

In each exercise some information is given. Use this information to name the segments that must be parallel. If there are no such segments, say so.

$m\angle 1+m\angle 2+m\angle 5+m\angle 6=180$

Short answer

The required segments are $\overline{PA}$and $\overline{LR}$.

Step-by-step solution

Step 1. Determine which theorem or postulate can be used

The theorem 3-6 can be used which states that the relation between two lines is parallel only when a separate line travels through these two lines and the angles which are positioned on the same side are supplementary which means that their measurement will be equal to if they are added.

Step 2. Make an observation from the provided figure

Write the provided angles according to the segments.

$m\angle APL+m\angle PLR=180$

The lines associated with these angles are $\overline{PA}$and $\overline{LR}$from which a separate line $\overline{PL}$travels.

Step 3. Make the conclusion

The obtained equation represents the angles that represent the same side interior angles so by using the theorem 3-6 determine the lines that are having a parallel relation between them.

$\overline{PA}||\overline{LR}$