Question

what is the measure of ∠prq?

Explanation:

Step1: Find ∠QPR

Since ∠NPR and ∠QPR are supplementary (they form a linear pair), we use the property that supplementary angles sum to \(180^\circ\). So, \(\angle QPR = 180^\circ - 108^\circ = 72^\circ\).

Step2: Find ∠PRQ

In triangle \(PQR\), the sum of the interior angles of a triangle is \(180^\circ\). We know \(\angle PQR = 62^\circ\) and \(\angle QPR = 72^\circ\). Let \(\angle PRQ = x\). Then, \(62^\circ + 72^\circ + x = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 62^\circ - 72^\circ = 46^\circ\).

Answer:

46