Question

2 quadrilateral mnpq is shown. what is ( mangle npq )? a not enough information b ( 134^{circ} ) c ( 78^{circ} ) d ( 102^{circ} )

Explanation:

Step1: Use the property of isosceles trapezoid

Since \(MN = PQ\) (marked as equal), \(MNPQ\) is an isosceles trapezoid. In an isosceles trapezoid, \(\angle NMQ+\angle NPQ = 180^{\circ}\) (supplementary angles).

Step2: Calculate \(\angle NMQ\)

\(\angle NMQ=32^{\circ}+46^{\circ}=78^{\circ}\)

Step3: Find \(\angle NPQ\)

Using \(\angle NMQ+\angle NPQ = 180^{\circ}\), we substitute \(\angle NMQ = 78^{\circ}\). Then \(\angle NPQ=180^{\circ}-\angle NMQ\). So \(\angle NPQ = 180^{\circ}-78^{\circ}=102^{\circ}\)

Answer:

D. \(102^{\circ}\)