Question

1. given that l || m and a || b, what are the values of x, y, and z?

Explanation:

Step1: Use corresponding - angles property

Since \(l\parallel m\) and \(a\parallel b\), the angle marked \(85^{\circ}\) and angle \(x\) are corresponding angles. So \(x = 85^{\circ}\).

Step2: Use vertical - angles property

The angle \(y\) and the \(85^{\circ}\) angle are vertical angles. Vertical angles are equal, so \(y=85^{\circ}\).

Step3: Use linear - pair property

The angle \(z\) and the \(85^{\circ}\) angle form a linear pair. A linear pair of angles sum to \(180^{\circ}\). So \(z = 180 - 85=95^{\circ}\).

Answer:

\(x = 85^{\circ},y = 85^{\circ},z = 95^{\circ}\)