Question

1. given the following two parallel lines cut by a transversal, which pair of angles represents alternate exterior angles? ∠4 and ∠8 ∠7 and ∠5 ∠1 and ∠2 ∠6 and ∠5

Explanation:

Step1: Recall alternate exterior angles definition

Alternate exterior angles are non - adjacent angles on opposite sides of the transversal and outside the two parallel lines.

Step2: Analyze each option

• For $\angle7$ and $\angle5$: These are interior angles (not exterior), so this is incorrect.
• For $\angle1$ and $\angle2$: These are adjacent angles (not alternate), so this is incorrect.
• For $\angle6$ and $\angle5$: These are adjacent angles (not alternate), so this is incorrect.
• For $\angle4$ and $\angle8$: $\angle4$ and $\angle8$ are non - adjacent, on opposite sides of the transversal, and outside the two parallel lines. So, $\angle4$ and $\angle8$ are alternate exterior angles.

Answer:

$\angle4$ and $\angle8$