Question

look at this diagram:
if mo and pr are parallel lines and m∠mnl = 126.9°, what is m∠pqs?

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Since \( \angle MNL\) and \( \angle PQR\) are vertical angles, \(m\angle PQR = m\angle MNL=126.9^{\circ}\)

Step2: Use the linear - pair property

\(\angle PQS\) and \(\angle PQR\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So, \(m\angle PQS + m\angle PQR=180^{\circ}\)
Substitute \(m\angle PQR = 126.9^{\circ}\) into the equation: \(m\angle PQS=180^{\circ}-m\angle PQR\)
\(m\angle PQS = 180^{\circ}- 126.9^{\circ}\)
\(m\angle PQS=53.1^{\circ}\)

Answer:

\(53.1^{\circ}\)