Question

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

Explanation:

Step1: Use corresponding - angles property

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

Step2: Use linear - pair property

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

Answer:

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