Question
If lines s and t are parallel, which pair of angles is supplementary and why?
(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
(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
Answers
GPT-4o mini
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.
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.