Question

find the measure of the indicated angle that makes u and v parallel. 50°. converse of the same - side interior angles theorem (converse ssi ∠s thm.). alternate exterior angles. 130°

Explanation:

Step1: Recall parallel - line angle relationships

When two lines are parallel, same - side interior angles are supplementary (add up to 180°). Given one angle is 130°. Let the indicated angle be \(x\).

Step2: Use the supplementary - angle formula

If two angles are same - side interior angles for parallel lines \(u\) and \(v\), then \(x + 130^{\circ}=180^{\circ}\). Solving for \(x\), we get \(x=180^{\circ}- 130^{\circ}=50^{\circ}\). Also, if we consider the alternate exterior angles relationship, when two lines are parallel, alternate exterior angles are equal. But the key here is using the converse of the same - side interior angles theorem.

Answer:

50°