Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the angle of \(55^{\circ}\) and \(x^{\circ}\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(x = 55\).

Step2: Use linear - pair property

The angle \(y^{\circ}\) and the \(55^{\circ}\) angle form a linear pair. A linear pair of angles is supplementary, that is \(y+55 = 180\). Solving for \(y\), we get \(y=180 - 55=125\).

Answer:

\(x = 55\), \(y = 125\)