Question

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Explanation:

Step1: Find the adjacent angle of \(152^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), if one angle is \(152^{\circ}\), then the adjacent angle \(y = 180^{\circ}-152^{\circ}\)

$$y = 28^{\circ}$$

Step2: Use the property of parallel lines (alternate - interior angles)

Assuming lines \(a\) and \(b\) are parallel. When a transversal intersects two parallel lines, alternate - interior angles are equal. Here, \(x\) and \(y\) are alternate - interior angles. So \(x=y\)

Answer:

\(x = 28\)