Question

question given parallelogram nopq below. if m∠prq = 74°, find m∠orp. answer attempt 1 out of 2 m∠orp = ° submit answer show examples

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, the diagonals bisect each other. Also, \(\angle PRQ\) and \(\angle ORP\) are adjacent angles that form a linear - pair.
The sum of angles in a linear - pair is \(180^{\circ}\).

Step2: Calculate \(m\angle ORP\)

We know that \(m\angle PRQ + m\angle ORP=180^{\circ}\).
Given \(m\angle PRQ = 74^{\circ}\), then \(m\angle ORP=180^{\circ}-m\angle PRQ\).
Substitute the value of \(m\angle PRQ\): \(m\angle ORP = 180 - 74\).
\(m\angle ORP=106^{\circ}\)

Answer:

\(106\)