Question

using parallel lines find the values of x and y. explain your reasoni 14.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Since \(x\) and the angle marked \(65^{\circ}\) are vertical angles, \(x = 65^{\circ}\).

Step2: Identify supplementary - angle relationship

The angle \(y\) and the \(65^{\circ}\) angle are adjacent and form a straight - line (linear pair). The sum of angles in a linear pair is \(180^{\circ}\). So \(y+65^{\circ}=180^{\circ}\), then \(y = 180^{\circ}-65^{\circ}=115^{\circ}\).

Answer:

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