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 \(\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles. Vertical angles are equal. So \(m\angle3 = m\angle1=61.8^{\circ}\)

Step2: Use the property of same - side interior angles

\(\angle3\) and \(\angle6\) are same - side interior angles. For parallel lines cut by a transversal, \(m\angle3 + m\angle6=180^{\circ}\) (same - side interior angles are supplementary)

Step3: Solve for \(m\angle6\)

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

Answer:

C. \(118.2^{\circ}\)