Question

in the picture below, line pq is parallel to line rs, and the lines are cut by a transversal, line tu. the transversal is not perpendicular to the parallel lines. which of the following are supplementary exterior angles? a. ∠e and ∠f b. ∠x and ∠e c. ∠h and ∠g d. ∠h and ∠e

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). Exterior angles are angles formed outside the two parallel lines.

Step2: Analyze each option

• Option A: \(\angle E\) and \(\angle F\) are adjacent angles on a straight - line (linear pair). But they are not exterior angles.
• Option B: \(\angle X\) is an interior angle (formed between the transversal and one of the parallel lines \(PQ\)) and \(\angle E\) is an exterior angle. They do not form a supplementary pair.
• Option C: \(\angle H\) and \(\angle G\) are adjacent angles on a straight - line (linear pair). But they are not exterior angles.
• Option D: \(\angle H\) and \(\angle E\) are exterior angles. Since \(PQ\parallel RS\) and \(TU\) is a transversal, \(\angle H\) and \(\angle E\) are on the same side of the transversal. By the property of parallel lines cut by a transversal, the sum of exterior angles on the same side of the transversal is \(180^{\circ}\).

Answer:

D. \(\angle H\) and \(\angle E\)