Question

look at this diagram:
if (overleftrightarrow{mo}) and (overleftrightarrow{pr}) are parallel lines and (mangle mnl = 137^{circ}), what is (mangle pqn)?
(square^{circ})

Explanation:

Step1: Identify the relationship between angles

Since \(\overleftrightarrow{MO}\) and \(\overleftrightarrow{PR}\) are parallel lines and \(SL\) is a transversal. \(\angle MNL\) and \(\angle PQN\) are supplementary angles (they form a linear - pair when considering the parallel lines and the transversal).
The formula for supplementary angles is \(m\angle MNL + m\angle PQN=180^{\circ}\)

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

Given \(m\angle MNL = 137^{\circ}\), substitute into the formula:
\(m\angle PQN=180^{\circ}-m\angle MNL\)
\(m\angle PQN = 180^{\circ}- 137^{\circ}\)
\(m\angle PQN=43^{\circ}\)

Answer:

\(43\)