Question

look at this diagram:
if ( overline{mo} ) and ( overline{pr} ) are parallel lines and ( mangle rqs = 127^{circ} ), what is ( mangle pqh )?

Explanation:

Step1: Find the measure of ∠PQR

Since ∠RQS and ∠PQR are supplementary angles (they form a linear - pair), and the sum of supplementary angles is \(180^{\circ}\).
If \(m\angle RQS = 127^{\circ}\), then \(m\angle PQR=180^{\circ}-m\angle RQS\)
\(m\angle PQR = 180^{\circ}-127^{\circ}=53^{\circ}\)

Step2: Use the property of parallel lines and alternate interior angles

Because \(MO\parallel PR\) and \(LS\) is a transversal, ∠PQH and ∠PQR are alternate interior angles. Alternate interior angles are equal when two parallel lines are cut by a transversal.

Answer:

\(53\)