two parallel lines are crossed by a transversal. if m∠1 = 61.8°, then what is the measure of m∠6? 61.8°…

Answer:

C. $118.2^{\circ}$

Explanation:

Step1: Identify angle - pair relationship

$\angle1$ and $\angle3$ are vertical angles, so $m\angle1 = m\angle3=61.8^{\circ}$.

Step2: Use the property of same - side interior angles

$\angle3$ and $\angle6$ are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., $m\angle3 + m\angle6=180^{\circ}$.

Step3: Calculate the measure of $\angle6$

$m\angle6 = 180^{\circ}-m\angle3$. Substitute $m\angle3 = 61.8^{\circ}$ into the equation: $m\angle6=180^{\circ}- 61.8^{\circ}=118.2^{\circ}$.