Question

determine the measure of ∠r.
figure is not drawn to scale

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle PQR\), we have \(\angle P+\angle Q+\angle R = 180^{\circ}\).

Step2: Substitute the known angles

We know that \(\angle P = 92^{\circ}\) and \(\angle Q=44^{\circ}\). Substituting these values into the equation \(\angle P+\angle Q+\angle R = 180^{\circ}\), we get \(92^{\circ}+44^{\circ}+\angle R=180^{\circ}\).

Step3: Solve for \(\angle R\)

First, add \(92^{\circ}\) and \(44^{\circ}\): \(92 + 44=136\). Then the equation becomes \(136^{\circ}+\angle R=180^{\circ}\). Subtract \(136^{\circ}\) from both sides: \(\angle R=180^{\circ}-136^{\circ}\).

Answer:

\(44^{\circ}\)