Question

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

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 \( \angle 1 \) and \( \angle 2 \): These are adjacent angles, likely linear or supplementary, not alternate interior.
• For \( \angle 7 \) and \( \angle 5 \): These are vertical angles (opposite angles formed by intersecting lines), not alternate interior.
• For \( \angle 4 \) and \( \angle 8 \): These are corresponding angles (same position relative to the parallel lines and transversal), not alternate interior.
• For \( \angle 6 \) and \( \angle 5 \): \( \angle 5 \) and \( \angle 6 \) lie between the two parallel lines (interior) and on opposite sides of the transversal, fitting the definition of alternate interior angles.

Answer:

\( \angle 6 \) and \( \angle 5 \)