Question

unit 2 angles & given m || n, find the value of x and y.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle of 144° and the angle adjacent to \(x\) are vertical angles, so the angle adjacent to \(x\) is 144°.

Step2: Use linear - pair property

A linear pair of angles sums to 180°. Since the angle adjacent to \(x\) is 144°, then \(x + 144^{\circ}=180^{\circ}\), so \(x=180 - 144=36^{\circ}\).

Step3: Use corresponding - angles property

Since \(m\parallel n\), the angle of 144° and \(y\) are corresponding angles. Corresponding angles of parallel lines are equal, so \(y = 144^{\circ}\).

Answer:

\(x = 36^{\circ},y = 144^{\circ}\)