Question

given m || n, find the value of x and y.

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the angle of \(142^{\circ}\) and \(x\) are corresponding angles. Corresponding angles of parallel lines are equal. So \(x = 142^{\circ}\).

Step2: Use linear - pair property

The angle \(x\) and \(y\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\). So \(y=180 - x\). Substitute \(x = 142^{\circ}\) into the equation, we get \(y = 180-142=38^{\circ}\).

Answer:

\(x = 142^{\circ}\), \(y = 38^{\circ}\)