To determine which pair of angles are supplementary when two parallel lines are intersected by a transversal (a horizontal line in this case), we need to understand the relationship between the angles created.
Two angles are defined as supplementary if their measures add up to 180 degrees.
- Linear Pair: If two angles are adjacent and formed by two intersecting lines, they sum to 180 degrees, making them supplementary.
- Corresponding Angles: These angles are equal when two parallel lines are cut by a transversal, so they cannot be supplementary.
- Consecutive Exterior Angles: These angles are also supplementary because if two parallel lines are cut by a transversal, each pair of consecutive exterior angles will sum to 180 degrees.
- Consecutive Interior Angles: These angles are not supplementary but equal when the angles are on the same side of the transversal.
Given the options:
- ∠G and ∠D are supplementary because they form a linear pair, which is a valid reasoning.
- ∠A and ∠B are corresponding angles and thus equal, not supplementary.
- ∠A and ∠D are consecutive exterior angles and would be supplementary, which is valid reasoning.
- ∠B and ∠G are consecutive interior angles and do not add up to 180 degrees.
The correct pair of supplementary angles would be the option that correctly identifies either ∠G and ∠D as they are a linear pair, or ∠A and ∠D as consecutive exterior angles.
If you have to choose one pair, the best answer based on the definition of each angle's relationship is:
∠G and ∠D because they are a linear pair.