Question

what is the measure of angle r? 29° 17° 31° 39°

Explanation:

Step1: Recall the triangle angle - sum theorem

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

Step2: Substitute the known angles

We know that \(\angle Q = 92^{\circ}\) and \(\angle S=59^{\circ}\). Substitute these values into the equation: \(92^{\circ}+59^{\circ}+\angle R=180^{\circ}\).

Step3: Solve for \(\angle R\)

First, calculate \(92 + 59=151\). Then the equation becomes \(151^{\circ}+\angle R=180^{\circ}\). Subtract \(151^{\circ}\) from both sides: \(\angle R=180^{\circ}-151^{\circ}\).

Answer:

\(29^{\circ}\)