Question

lines m and n are parallel. find the measure of \\( \angle b \\).

Explanation:

Step1: Use the property of corresponding angles

Since lines \(M\) and \(N\) are parallel, the angle of \(30^{\circ}\) and the angle adjacent to \(\angle b\) (on the same side of the transversal) are corresponding angles.

Step2: Use the linear - pair property

The angle adjacent to \(\angle b\) and \(\angle b\) form a linear pair. We know that the sum of angles in a linear pair is \(180^{\circ}\). Let the angle adjacent to \(\angle b\) be \(x = 30^{\circ}\) (by corresponding angles). Then, using the formula \(x+\angle b=180^{\circ}\), we substitute \(x = 30^{\circ}\) into the formula: \(\angle b=180^{\circ}-30^{\circ}\)

Answer:

\(150\)