Question

1. given the following two parallel lines cut by a transversal. which pair of angles represents alternate interior angles? ∠7 and ∠8, ∠3 and ∠8, ∠7 and ∠2, ∠4 and ∠8

Explanation:

To determine alternate interior angles, we recall the definition: alternate interior angles are formed when a transversal crosses two parallel lines, and they lie between the two parallel lines (interior) and on opposite sides of the transversal (alternate).

• For $\angle7$ and $\angle8$: These are adjacent angles (linear pair), not alternate interior.
• For $\angle3$ and $\angle8$: $\angle3$ is above the top parallel line (exterior relative to the two lines), so not interior.
• For $\angle7$ and $\angle2$: $\angle7$ is below the bottom parallel line, $\angle2$ is above the top parallel line—neither is between the two lines.
• For $\angle4$ and $\angle8$: $\angle4$ and $\angle8$ lie between the two parallel lines (interior) and on opposite sides of the transversal (alternate), matching the definition of alternate interior angles.

Answer:

$\boldsymbol{\angle4}$ and $\boldsymbol{\angle8}$ (assuming the option with $\angle4$ and $\angle8$ is the correct choice; if the options are labeled, e.g., the teal option, that would be the answer).