Question

a geometric construction is shown. if m∠cqr = 30, what is the measure of ∠pqr? 10 15 30 60

Explanation:

Step1: Observe the geometric construction

The construction shows that ray $QC$ is the angle - bisector of $\angle PQR$.

Step2: Use the property of angle - bisector

If $QC$ is the angle - bisector of $\angle PQR$, then $\angle PQR = 2\angle CQR$.
Since $\angle CQR=30^{\circ}$, we have $\angle PQR = 2\times30^{\circ}$.

Answer:

D. $60^{\circ}$