Question

1. in the diagram shown, line q is parallel to line r. both are crossed by line s. the eight angles formed when the parallel lines are crossed by line s are labeled. answer the following: (a) list two angles that form an alternate interior angle pair. (b) what angle corresponds to ∠8? (c) give two angles that form a same side interior pair. what is the relationship between these two angles?

Explanation:

Step1: Recall alternate - interior angles

Alternate - interior angles are between the two parallel lines and on opposite sides of the transversal. $\angle 3$ and $\angle 5$ is a valid alternate - interior angle pair.

Step2: Recall corresponding angles

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. $\angle 4$ and $\angle 8$ are corresponding angles.

Step3: Recall same - side interior angles

Same - side interior angles are between the two parallel lines and on the same side of the transversal. For example, $\angle 3$ and $\angle 7$ are same - side interior angles. The relationship between same - side interior angles of parallel lines is that they are supplementary (their sum is $180^{\circ}$).

Answer:

(a) $\angle 3$ and $\angle 5$
(b) $\angle 4$
(c) $\angle 3$ and $\angle 7$, they are supplementary.