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

∠G and ∠D because they are a linear pair
∠G and ∠D because they are a linear pair

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

∠A and ∠B because they are corresponding angles

Answer 1

To determine which pair of angles is supplementary, we need to analyze the relationship between the given angles and the properties of parallel lines cut by a transversal.

When two parallel lines (s and t) are cut by a transversal (the horizontal line), certain angle relationships are established:

1. **Consecutive interior angles** (interior angles on the same side of the transversal) are supplementary.
2. **Linear pairs** are supplementary because they add up to 180 degrees.
3. **Corresponding angles** are equal, not supplementary.

Given the options:

- **∠A and ∠D because they are consecutive exterior angles**: This is incorrect because consecutive exterior angles are not supplementary.
- **∠G and ∠D because they are a linear pair**: This is likely correct as linear pairs are supplementary.
- **∠B and ∠G because they are consecutive interior angles**: This is incorrect unless specifically noted in the layout, as we generally look for angles on the same side of the transversal.
- **∠A and ∠B because they are corresponding angles**: This is incorrect since corresponding angles are equal.

Therefore, the correct answer is:

**∠G and ∠D because they are a linear pair.**