Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the angle of \(47^{\circ}\) and \(x\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(x = 47\).

Step2: Use linear - pair property

\(x\) and \(y\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\), that is \(x + y=180\). Substitute \(x = 47\) into the equation: \(y=180 - x\). Then \(y = 180-47=133\).

Answer:

\(x = 47\), \(y = 133\)