Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle of 65° and \(y\) are vertical angles. So \(y = 65^{\circ}\).

Step2: Use supplementary - angle property for parallel lines

Since \(m\parallel n\), \(x\) and \(y\) are supplementary angles (same - side interior angles). The sum of supplementary angles is 180°. So \(x=180 - y\). Substitute \(y = 65^{\circ}\) into the equation, we get \(x=180 - 65=115^{\circ}\).

Answer:

\(x = 115^{\circ}\), \(y = 65^{\circ}\)