Question

find $m\angle p$. the diagram is not to scale.

74
64
84
106

Explanation:

Step1: Find the adjacent angle of \(106^{\circ}\)

When two lines are cut by a transversal, adjacent angles on a straight - line sum to \(180^{\circ}\). Let the adjacent angle of \(106^{\circ}\) be \(x\). Then \(x + 106^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-106^{\circ}=74^{\circ}\).

Step2: Use the property of parallel lines

Since lines \(g\) and \(h\) are parallel and cut by transversal \(j\), \(\angle P\) and the angle \(x\) (which we found to be \(74^{\circ}\)) are congruent (corresponding angles).

Answer:

\(74\)