Question

given that lines a and b are parallel and that m∠6 = 74°, find m∠1. a 16° b 76° c 96° d 106° e 116°

Explanation:

Step1: Find the measure of ∠3

Since lines \(a\) and \(b\) are parallel, \(\angle3\) and \(\angle6\) are alternate - interior angles. So \(m\angle3=m\angle6 = 74^{\circ}\)

Step2: Find the measure of ∠1

\(\angle1\) and \(\angle3\) are supplementary angles (they form a linear pair). Using the formula \(m\angle1 + m\angle3=180^{\circ}\)
Substitute \(m\angle3 = 74^{\circ}\) into the formula: \(m\angle1=180^{\circ}-m\angle3\)
\(m\angle1 = 180^{\circ}-74^{\circ}=106^{\circ}\)

Answer:

D. \(106^{\circ}\)