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 \(x = 47^{\circ}\).

Step2: Use linear - pair property

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

Answer:

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