Question

find the largest angle of △pqr. assume that v is a positive number.

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side.

Step2: Identify the longest side

Given side lengths \(15v\) and \(46v\). Since \(v>0\), \(46v>15v\). The angle opposite the side \(46v\) is \(\angle Q\). Also, we are given that \(\angle R = 92^{\circ}\).

Step3: Compare angles

Since the sum of angles in a triangle is \(180^{\circ}\), and we know one angle is \(92^{\circ}\), and the largest - angle - opposite - longest - side rule. The angle \(\angle Q\) is the largest angle as the side opposite it (\(46v\)) is the longest side among the two given non - hypotenuse sides and \(\angle R=92^{\circ}\) is already an obtuse angle. In a triangle, an obtuse angle is the largest angle. And among the non - given angles, the one opposite the longer non - hypotenuse side contributes to the overall largest angle situation.

Answer:

\(\angle Q\)