Question

on a map, haven rd and pine rd are parallel, and mills rd is a transversal. how can the value of x be determined? alternate exterior angles are supplementary, so x = 43°. corresponding angles are congruent, so x = 43°. corresponding angles are supplementary, so x = 137°. alternate exterior angles are congruent, so x = 137°.

Explanation:

Step1: Recall angle theorems for parallel lines

When two parallel lines are cut by a transversal, alternate exterior angles are congruent, and corresponding angles are congruent. Also, consecutive interior angles are supplementary.

Step2: Analyze the angles

The angle of \(137^\circ\) and the angle adjacent to it (forming a linear pair) is \(43^\circ\) (since \(180 - 137=43\)). Now, looking at the position of \(x\) and the \(137^\circ\) angle, they are alternate exterior angles. By the alternate exterior angles theorem, alternate exterior angles are congruent. So \(x = 137^\circ\) because alternate exterior angles are congruent.

Answer:

Alternate exterior angles are congruent, so \(x = 137^\circ\) (the last option: Alternate exterior angles are congruent, so \(x = 137^\circ\)).