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 ∠9 and ∠11 are supplementary angles (they form a linear pair), and \(m\angle9 + m\angle11=180^{\circ}\), given \(m\angle9 = 97^{\circ}\), then \(m\angle11=180^{\circ}-97^{\circ}=83^{\circ}\).

Step2: Use the property of parallel lines

Lines \(e\) and \(f\) are parallel, and transversal \(d\) cuts them. ∠11 and ∠15 are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So \(m\angle15=m\angle11\).

Answer:

\(m\angle15 = 83^{\circ}\) (the second option)