Question

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

Explanation:

Step1: Recall angle - relationship

When two parallel lines \(m\) and \(n\) are cut by a transversal, the corresponding angles are equal, the alternate - interior angles are equal, and the same - side interior angles are supplementary. The \(167^{\circ}\) angle and the angle adjacent to \(x^{\circ}\) are same - side interior angles.

Step2: Use the supplementary - angle property

Since same - side interior angles of parallel lines are supplementary (their sum is \(180^{\circ}\)), if we let the angle adjacent to \(x^{\circ}\) be \(y^{\circ}\), then \(y + 167=180\). Solving for \(y\), we get \(y = 180 - 167=13^{\circ}\).

Step3: Find the value of \(x\)

The angle \(x\) and \(y\) are vertical angles. Vertical angles are equal. So \(x=y\). Since \(y = 13^{\circ}\), then \(x = 13^{\circ}\).

Answer:

\(13\)