Question
Proofs About Angles Quick Check
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Question
Use the image to answer the question.
A horizontal line is intersected by two parallel lines lower s and lower t that slant from left to right forming eight angles.
If lines s and t are parallel, which pair of angles is supplementary and why?
(1 point)
Responses which answer is correct and more accurate
∠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
∠G
and ∠D
because they are a linear pair
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Answers
GPT-4o mini
To determine which pair of angles is supplementary, we need to understand the definitions of the angle relationships among parallel lines cut by a transversal.
Given two parallel lines (lines \( s \) and \( t \)) intersected by a transversal (the horizontal line), the pairs of angles formed include corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
1. **Consecutive Interior Angles** are two angles that are on the same side of the transversal and inside the parallel lines. They are supplementary, meaning their sum is 180 degrees.
2. **Corresponding Angles** are found in matching positions when the lines are crossed by a transversal. They are congruent, not supplementary.
3. **Exterior Angles** are formed outside the parallel lines by the transversal.
4. **Linear Pair** refers to two adjacent angles that sum to 180 degrees, but they need to be on the same line.
Based on this, the proper answer would be:
**∠G and ∠D because they are a linear pair.**
This is correct because angles \( G \) and \( D \) are adjacent and form a straight line, hence supplementary.
Given two parallel lines (lines \( s \) and \( t \)) intersected by a transversal (the horizontal line), the pairs of angles formed include corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
1. **Consecutive Interior Angles** are two angles that are on the same side of the transversal and inside the parallel lines. They are supplementary, meaning their sum is 180 degrees.
2. **Corresponding Angles** are found in matching positions when the lines are crossed by a transversal. They are congruent, not supplementary.
3. **Exterior Angles** are formed outside the parallel lines by the transversal.
4. **Linear Pair** refers to two adjacent angles that sum to 180 degrees, but they need to be on the same line.
Based on this, the proper answer would be:
**∠G and ∠D because they are a linear pair.**
This is correct because angles \( G \) and \( D \) are adjacent and form a straight line, hence supplementary.