Proofs About Angles Quick Check

Question

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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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Answer 1

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.