Question

consider the diagram shown. complete the statements. if the measures of ∠6 and ∠8 are equal, then lines are parallel. if the measures of angles ∠6 and ∠10 add up to 180°, then lines are parallel.

Explanation:

Step1: Recall angle - parallel line relationships

If two alternate - interior angles are equal, the lines are parallel. $\angle6$ and $\angle8$ are alternate - interior angles formed by lines $p$ and $q$ and transversal $r$.

Step2: Recall another angle - parallel line relationship

If two same - side interior angles are supplementary (add up to 180°), the lines are parallel. $\angle6$ and $\angle10$ are same - side interior angles formed by lines $r$ and $s$ and transversal $p$.

Answer:

If the measures of $\angle6$ and $\angle8$ are equal, then lines $p$ and $q$ are parallel.
If the measures of angles $\angle6$ and $\angle10$ add up to 180°, then lines $r$ and $s$ are parallel.