Question

note: figure not drawn to scale. given rectangle nopq and triangle prq share side pq, solve for m∠qrp. (a) 30° (b) 60° (c) 100° (d) 120°

Explanation:

Step1: Identify triangle properties

Since \(PR = QR\) (marked with equal - length symbols), \(\triangle PRQ\) is isosceles. Let's assume some additional properties from the figure. If we consider the symmetry and the fact that we may be able to use angle - sum properties of a triangle.

Step2: Recall angle - sum of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In an isosceles triangle \(\triangle PRQ\) with \(PR = QR\), let \(\angle QRP=\angle RPQ = x\).

Step3: Analyze the figure for more information

Although not all information is given explicitly, if we assume that the triangle is equilateral (a special case of isosceles where all sides are equal). Since \(PQ = 4\) and if we assume \(PR = QR=PQ = 4\) (from the equal - length markings and the context), then \(\triangle PRQ\) is equilateral.
In an equilateral triangle, each interior angle is \(60^{\circ}\). So \(m\angle QRP = 60^{\circ}\).

Answer:

B. \(60^{\circ}\)