Proofs About Angles Quick Check

Question

3 of 53 of 5 Items

WHICH ANSWER IS MORE ACCURATE AND Why

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

∠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
Skip to navigation

Answer 1

To determine which pair of angles is supplementary, we need to review the definitions:

1. Supplementary Angles: Two angles are supplementary if their measures add up to 180 degrees.

2. Consecutive Exterior Angles: Alternate exterior angles that are on the same side of the transversal. They are not supplementary.

3. Corresponding Angles: Angles that are in the same position with respect to the two parallel lines and the transversal. They are equal, not supplementary.

4. Consecutive Interior Angles: Angles that are on the same side of the transversal, between the two parallel lines. They are supplementary.

5. Linear Pair: Two adjacent angles that form a straight line (add up to 180 degrees).

Given the options in your question, let's analyze them:

• ∠A and ∠D: If they are consecutive exterior angles, they are not supplementary.

• ∠A and ∠B: These would be corresponding angles if they are in the same position related to lines s and t. Therefore, they are equal, not supplementary.

• ∠B and ∠G: If these angles are consecutive interior angles, they are supplementary.

• ∠G and ∠D: If they form a linear pair, they are supplementary.

Given the premise that lines s and t are parallel and intersected by a transversal, the following pairs are valid options:

• If ∠B and ∠G are indeed consecutive interior angles, they must be supplementary.
• If ∠G and ∠D are adjacent and form a linear pair, they are also supplementary.

Without knowing the specific configuration, if either option is applicable, both might be correct based on usual geometric definitions.

However, since the problem is looking for a specific correct answer based on your question, the more common answer in the context of parallel lines intersected by a transversal would be ∠B and ∠G because they are consecutive interior angles. This is generally emphasized in geometry as these angles are always supplementary when two parallel lines are crossed by a transversal.