Question

look at this diagram:
if \\( \overleftrightarrow { m o } \\) and \\( \overleftrightarrow { p r } \\) are parallel lines and \\( m \angle m n q = 1 1 4 ^ { \circ } \\), what is \\( m \angle m n l \\)?

Explanation:

Step1: Use the linear - pair relationship

We know that \(\angle MNQ\) and \(\angle MNL\) form a linear pair.
The formula for the sum of angles in a linear pair is \(m\angle MNQ + m\angle MNL=180^{\circ}\).

Step2: Solve for \(m\angle MNL\)

Given \(m\angle MNQ = 114^{\circ}\), we substitute into the formula:
\(m\angle MNL=180^{\circ}-m\angle MNQ\).
\(m\angle MNL = 180^{\circ}- 114^{\circ}\).
\(m\angle MNL=66^{\circ}\).

Answer:

\(66^{\circ}\)