Question

in triangle pqr, $overline{qr}$ is extended to point s. the measure of $angle pqr$ is $132^{circ}$, and the measure of $angle prs$ is $166^{circ}$. what is the measure of $angle qpr$? a $14^{circ}$ b $24^{circ}$ c $34^{circ}$ d $48^{circ}$

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle PQR\), \(\angle PRS\) is an exterior angle and \(\angle QPR\) and \(\angle PQR\) are non - adjacent interior angles. So, \(\angle PRS=\angle QPR+\angle PQR\).

Step2: Solve for \(\angle QPR\)

We know that \(\angle PQR = 132^{\circ}\) and \(\angle PRS=166^{\circ}\). Rearranging the formula \(\angle QPR=\angle PRS - \angle PQR\). Substitute the given values: \(\angle QPR=166^{\circ}-132^{\circ}\).
\(\angle QPR = 34^{\circ}\)

Answer:

C. \(34^{\circ}\)