Question

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

Explanation:

Step1: Recall angle - parallel line relationships

When two lines are cut by a transversal, if corresponding angles are equal, the lines are parallel. ∠6 and ∠8 are corresponding angles for lines r and s with transversal q. So, if ∠6 = ∠8, then r∥s.

Step2: Recall another angle - parallel line relationship

When two lines are cut by a transversal, if same - side interior angles are supplementary (add up to 180°), the lines are parallel. ∠6 and ∠10 are same - side interior angles for lines r and s with transversal p. So, if ∠6+∠10 = 180°, then r∥s.

Answer:

If the measures of ∠6 and ∠8 are equal, then lines r and s are parallel. If the measures of angles ∠6 and ∠10 add up to 180°, then lines r and s are parallel.