Question

If lines s and t are parallel, which pair of angles is supplementary and why?

a. ∠A and ∠D because they are consecutive exterior angles
b. ∠G and ∠D because they are a linear pair
c. ∠A and ∠B because they are corresponding angles
d. ∠B and ∠G because they are consecutive interior angles

Answer 1

To determine which pair of angles is supplementary when lines \( s \) and \( t \) are parallel, we need to understand the relationships between the angles formed when two parallel lines are intersected by a transversal.

Let's analyze each option:

a. **∠A and ∠D because they are consecutive exterior angles** - This statement is correct in identifying the angles as exterior angles, but consecutive exterior angles are not supplementary. Therefore, this option is not valid.

b. **∠G and ∠D because they are a linear pair** - A linear pair refers to two adjacent angles that sum to 180 degrees. If ∠G and ∠D are a linear pair, they are supplementary. This option is potentially valid depending on their placement.

c. **∠A and ∠B because they are corresponding angles** - Corresponding angles formed by a transversal intersecting parallel lines are congruent (not supplementary). Hence, this option is invalid.

d. **∠B and ∠G because they are consecutive interior angles** - Consecutive interior angles are also not supplementary; they are equal due to the parallel lines.

Among these options, **option b** likely represents the correct relationship if ∠G and ∠D are indeed on the same side of the transversal and adjacent. Thus, the correct answer is:

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