Question

two parallel lines are crossed by a transversal. if ( mangle6 = 123.5^{circ}), then ( mangle1) is ( 67.5^{circ}), ( 123.5^{circ}), ( 56.5^{circ}), ( 136.5^{circ})

Explanation:

Step1: Find the measure of ∠3

Since \(x\parallel y\), \(\angle3\) and \(\angle6\) are alternate interior angles. Alternate interior angles are equal. So \(m\angle3 = m\angle6=123.5^{\circ}\)

Step2: Find the measure of ∠1

\(\angle1\) and \(\angle3\) are supplementary angles (they form a linear - pair). The sum of supplementary angles is \(180^{\circ}\). So \(m\angle1=180^{\circ}-m\angle3\)
Substitute \(m\angle3 = 123.5^{\circ}\) into the formula: \(m\angle1=180 - 123.5=56.5^{\circ}\)

Answer:

\(56.5^{\circ}\)