Question

1. name two pairs of alternate interior angles.
2. what is the relationship between ∠2 and ∠8?
3. which postulate or theorem justifies that ∠3 is supplementary to ∠6?
4. which postulate or theorem justifies that m∠4 is equal to m∠8?

Explanation:

Step1: Recall linear - pair property

When two lines intersect, adjacent angles on a straight - line form a linear pair and are supplementary. $\angle3$ and $\angle6$ are adjacent angles on a straight - line formed by the intersection of the two transversals. So, the Linear Pair Postulate justifies that $\angle3$ is supplementary to $\angle6$.

Step2: Recall corresponding - angles property

Corresponding angles are congruent when two parallel lines are cut by a transversal. $\angle4$ and $\angle8$ are corresponding angles. So, the Corresponding Angles Postulate justifies that $m\angle4=m\angle8$.

Answer:

1. Linear Pair Postulate
2. Corresponding Angles Postulate