Question

look at this diagram: if \\( \overleftrightarrow{mo} \\) and \\( \overleftrightarrow{pr} \\) are parallel lines and \\( m\angle mnq = 114 ^ { \circ } \\), what is \\( m\angle onl? \\)

Explanation:

Step1: Use the linear - pair relationship

Since \(\angle MNQ\) and \(\angle QNO\) form a linear pair (they are adjacent angles on a straight line), we know that \(m\angle MNQ + m\angle QNO=180^{\circ}\). Given \(m\angle MNQ = 114^{\circ}\), then \(m\angle QNO=180^{\circ}-114^{\circ}\).

$$m\angle QNO = 180 - 114=66^{\circ}$$

Step2: Use the vertical - angle relationship

\(\angle ONL\) and \(\angle QNO\) are vertical angles. Vertical angles are equal. So \(m\angle ONL=m\angle QNO\).

Answer:

\(66\)