Question

two parallel lines are crossed by a transversal. what is the value of x? x = 45 x = 65 x = 95 x = 115

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are crossed by a transversal, consecutive interior angles are supplementary. That is, their sum is \(180^{\circ}\).
Let the angle of \(115^{\circ}\) and \(x^{\circ}\) be consecutive interior angles. So, \(115 + x=180\).

Step2: Solve for \(x\)

Subtract \(115\) from both sides of the equation \(115 + x=180\).
\(x=180 - 115\)
\(x = 65\)

Answer:

\(x = 65\) (the second option)