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 \(y\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are equal. So \(y = 142\).

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 \(x=180 - y\). Substitute \(y = 142\) into the equation, we get \(x=180 - 142=38\).

Answer:

\(x = 38\), \(y = 142\)