Question

1. what are the alternate exterior angle pairs in the picture below?

○ ∠1 and ∠3, ∠5 and ∠7
○ ∠1 and ∠7, ∠2 and ∠8
○ ∠1 and ∠8, ∠2 and ∠7
○ ∠1 and ∠2, ∠7 and ∠8

Explanation:

To determine alternate exterior angles, we recall the definition: alternate exterior angles are two angles that lie outside the two lines (here, lines \( r \) and \( s \)) and on opposite sides of the transversal (line \( q \)).

• For \( \angle 1 \) and \( \angle 7 \): \( \angle 1 \) is outside lines \( r \) and \( s \) (above \( r \)) and \( \angle 7 \) is outside lines \( r \) and \( s \) (below \( s \)), and they are on opposite sides of transversal \( q \).
• For \( \angle 2 \) and \( \angle 8 \): \( \angle 2 \) is outside lines \( r \) and \( s \) (above \( r \)) and \( \angle 8 \) is outside lines \( r \) and \( s \) (below \( s \)), and they are on opposite sides of transversal \( q \).

Let's analyze other options:

• \( \angle 1 \) and \( \angle 3 \), \( \angle 5 \) and \( \angle 7 \): These are vertical angles or alternate interior, not exterior.
• \( \angle 1 \) and \( \angle 8 \), \( \angle 2 \) and \( \angle 7 \): Do not meet the alternate exterior criteria (wrong sides or positions).
• \( \angle 1 \) and \( \angle 2 \), \( \angle 7 \) and \( \angle 8 \): These are adjacent or vertical angles, not alternate exterior.

So the correct pair is \( \angle 1 \) and \( \angle 7 \), \( \angle 2 \) and \( \angle 8 \).

Answer:

\( \boldsymbol{\angle 1} \) and \( \boldsymbol{\angle 7} \), \( \boldsymbol{\angle 2} \) and \( \boldsymbol{\angle 8} \) (the option with \( \angle 1 \) and \( \angle 7 \), \( \angle 2 \) and \( \angle 8 \))