Question

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Explanation:

Step1: Use the property of parallel lines and transversals

When two parallel lines are cut by a transversal, corresponding angles and supplementary angles are used. Here, the angle \(x\) and the \(75^{\circ}\) angle are related as \(x + 75^{\circ}=180^{\circ}\) (they are same - side interior angles for the parallel lines).

Step2: Solve for \(x\)

Subtract \(75^{\circ}\) from both sides of the equation \(x + 75^{\circ}=180^{\circ}\). So, \(x=180^{\circ}-75^{\circ}\).

Answer:

\(x = 105^{\circ}\)