Question

look at this diagram:
if ( overline{mo} ) and ( overline{pr} ) are parallel lines and ( mangle pqs = 121^circ ), what is ( mangle rqn )?

Explanation:

Step1: Find the measure of the adjacent angle to \(\angle PQS\)

Since \(\angle PQS\) and \(\angle RQL\) are adjacent angles on a straight - line, and the sum of adjacent angles on a straight - line is \(180^{\circ}\). Let \(m\angle RQL=x\). Then \(x + 121^{\circ}=180^{\circ}\), so \(x=\angle RQL = 180^{\circ}-121^{\circ}=59^{\circ}\).

Step2: Use the property of parallel lines

Because \(MO\parallel PR\) and \(SL\) is a transversal, \(\angle RQL\) and \(\angle RQN\) are vertical angles. Vertical angles are equal.

Answer:

\(59^{\circ}\)