Question

two parallel lines are crossed by a transversal. if ( mangle1 = 61.8^{circ} ), then what is the measure of ( mangle6 )? ( 61.8^{circ} ) ( 81.8^{circ} ) ( 118.2^{circ} ) ( 128.2^{circ} )

Explanation:

Step1: Find the measure of ∠3

Since ∠1 and ∠3 are vertical angles, \(m\angle3 = m\angle1=61.8^{\circ}\)

Step2: Use the property of same - side interior angles

Because \(x\parallel y\) and \(w\) is a transversal, \(\angle3\) and \(\angle6\) are same - side interior angles. The sum of same - side interior angles is \(180^{\circ}\). So \(m\angle3 + m\angle6=180^{\circ}\)

Step3: Solve for \(m\angle6\)

Substitute \(m\angle3 = 61.8^{\circ}\) into \(m\angle3 + m\angle6=180^{\circ}\), we get \(m\angle6=180^{\circ}-m\angle3\). Then \(m\angle6 = 180^{\circ}- 61.8^{\circ}=118.2^{\circ}\)

Answer:

\(118.2^{\circ}\)