Question

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Explanation:

Step1: Find the alternate - interior angle

Since the two lines are parallel, the alternate - interior angle of the \(30^{\circ}\) angle is also \(30^{\circ}\).

Step2: Use the angle - sum property of a straight line

We know that the sum of angles on a straight line is \(180^{\circ}\). Let the angle adjacent to \(x\) be \(y\). Then \(y = 30^{\circ}\) (alternate - interior angles). And \(x + y=180^{\circ}\) (linear pair). Substituting \(y = 30^{\circ}\) into the equation, we get \(x=180^{\circ}-30^{\circ}\).

Answer:

\(x = 150^{\circ}\)