When lines s and t are parallel, the angles that are supplementary must be either consecutive interior angles, consecutive exterior angles, or a linear pair of angles.
Based on the provided options, here’s the analysis of each:
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∠A and ∠B because they are corresponding angles: Corresponding angles are equal when the lines are parallel, not supplementary.
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∠B and ∠G because they are consecutive interior angles: Consecutive interior angles are supplementary when the lines are parallel, making this a valid choice.
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∠G and ∠D because they are a linear pair: Linear pairs of angles are always supplementary, so this is also a valid choice.
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∠A and ∠D because they are consecutive exterior angles: Consecutive exterior angles are supplementary when the lines are parallel. So, this option is also valid.
From the given options, the pairs that are supplementary because of the reasons provided are:
- ∠B and ∠G because they are consecutive interior angles
- ∠G and ∠D because they are a linear pair
- ∠A and ∠D because they are consecutive exterior angles
If you have to choose one from the responses, ∠B and ∠G because they are consecutive interior angles is a clear example of supplementary angles formed by parallel lines.