Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), \(x\) and the \(137^{\circ}\) angle are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are equal. So \(x = 137^{\circ}\).

Step2: Use linear - pair property

\(x\) and \(y\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\). So \(y=180 - x\). Substituting \(x = 137^{\circ}\), we get \(y = 180-137=43^{\circ}\).

Answer:

\(x = 137\), \(y = 43\)