If lines s and t are parallel, which pair of angles is supplementary and why?

Question

(1 point)
Responses
which answers are accurate and why by asking questions to your teacher
∠A
and ∠D
because they are consecutive exterior angles
∠A
and ∠D
because they are consecutive exterior angles

∠A
and ∠B
because they are corresponding angles
∠A
and ∠B
because they are corresponding angles

∠B
and ∠G
because they are consecutive interior angles
∠B
and ∠G
because they are consecutive interior angles

∠G
and ∠D
because they are a linear pair

Answer 1

To determine which pair of angles is supplementary when lines \( s \) and \( t \) are parallel, let's analyze the angle relationships:

1. Consecutive Exterior Angles: Angles \( \angle A \) and \( \angle D \) are consecutive exterior angles. However, consecutive exterior angles are not necessarily supplementary when lines are parallel; they are congruent instead.

2. Corresponding Angles: Angles \( \angle A \) and \( \angle B \) are corresponding angles. Corresponding angles are congruent when the lines are parallel, so they are not supplementary.

3. Consecutive Interior Angles: Angles \( \angle B \) and \( \angle G \) are consecutive interior angles. When lines are parallel, consecutive interior angles are supplementary (they add up to 180 degrees).

4. Linear Pair: Angles \( \angle G \) and \( \angle D \) can be a linear pair if they lie on a straight line. Linear pairs are always supplementary, but without knowing the exact configuration, we can't confirm if this is the case.

Based on this analysis, the correct choice for a pair of supplementary angles when lines \( s \) and \( t \) are parallel is:

\( \angle B \) and \( \angle G \) because they are consecutive interior angles.

This is the only pair that is guaranteed to be supplementary due to the properties of parallel lines and transversal angles.