Question

if \\( \overleftrightarrow { oq } \\) and \\( \overleftrightarrow { rt } \\) are parallel lines and \\( m \angle q p n = 42 ^ { \circ } \\), what is \\( m \angle o p n \\)?

Explanation:

Step1: Analyze the relationship between angles

Since \(\overrightarrow{OQ}\) and \(\overrightarrow{RT}\) are parallel lines, and \(\angle QPN\) and \(\angle OPN\) form a linear - pair.

Step2: Use the linear - pair property

The sum of angles in a linear - pair is \(180^{\circ}\). If \(m\angle QPN = 42^{\circ}\), and \(m\angle QPN+m\angle OPN = 180^{\circ}\).
Then \(m\angle OPN=180^{\circ}-m\angle QPN\).
Substitute \(m\angle QPN = 42^{\circ}\) into the formula: \(m\angle OPN = 180 - 42\).

Answer:

\(138\)