Question

what value of x will ensure that lines a and b are parallel?

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines are cut by a transversal, same - side interior angles are supplementary. That is, if lines \(a\) and \(b\) are parallel, then \(x + 127^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

Subtract \(127^{\circ}\) from both sides of the equation \(x + 127^{\circ}=180^{\circ}\).
\(x=180^{\circ}-127^{\circ}\)
\(x = 53^{\circ}\)

Answer:

\(53^{\circ}\)