Question

two parallel lines, e and f, are crossed by two transversals. what is the measure of ∠15? m∠15 = 77° m∠15 = 83° m∠15 = 93° m∠15 = 97°

Explanation:

Step1: Find the measure of ∠11

Since ∠12 and ∠11 are adjacent angles on a straight - line, \(m\angle11 + m\angle12=180^{\circ}\). Given \(m\angle12 = 97^{\circ}\), then \(m\angle11=180^{\circ}-97^{\circ}=83^{\circ}\).

Step2: Use the property of parallel lines

Lines \(e\) and \(f\) are parallel and \(d\) is a transversal. ∠11 and ∠15 are alternate interior angles. For parallel lines \(e\parallel f\) and transversal \(d\), alternate interior angles are equal. So \(m\angle15=m\angle11\).

Answer:

\(m\angle15 = 83^{\circ}\)