Question

if lines s and t are parallel, which pair of angles is supplementary and why? (1 point) ∠g and ∠d because they are a linear pair ∠b and ∠g because they are consecutive interior angles ∠a and ∠d because they are consecutive exterior angles ∠a and ∠b because they are corresponding angles

Explanation:

Step1: Recall linear pair definition

A linear pair of angles is adjacent and their non - common sides form a straight line. So, their sum is \(180^{\circ}\). For \(\angle G\) and \(\angle D\), they are adjacent and form a straight line. But we need to check other options based on parallel line properties.

Step2: Recall consecutive interior angles property

When two parallel lines \(s\) and \(t\) are cut by a transversal (the horizontal line in the figure), consecutive interior angles are supplementary. \(\angle B\) and \(\angle G\) are not consecutive interior angles.

Step3: Recall consecutive exterior angles property

Consecutive exterior angles are supplementary when two parallel lines are cut by a transversal. \(\angle A\) and \(\angle D\) are consecutive exterior angles. Since \(s\parallel t\), by the consecutive exterior angles theorem, \(\angle A+\angle D = 180^{\circ}\).

Step4: Recall corresponding angles property

Corresponding angles are equal when two parallel lines are cut by a transversal. \(\angle A\) and \(\angle B\) are not corresponding angles.

Answer:

\(\angle A\) and \(\angle D\) because they are consecutive exterior angles.