Question

in circle q with m∠pqr = 84°, find the m∠psr.

Explanation:

Step1: Recall the central angle theorem

The measure of an inscribed angle is half the measure of its intercepted central angle. Here, $\angle PQR$ is a central angle intercepting arc $PR$, and $\angle PSR$ is an inscribed angle intercepting the same arc $PR$.

Step2: Apply the theorem

Given $m\angle PQR = 84^\circ$, then the measure of the inscribed angle $\angle PSR$ is half of that. So, $m\angle PSR=\frac{1}{2}\times m\angle PQR$.
Substitute $m\angle PQR = 84^\circ$ into the formula: $m\angle PSR=\frac{1}{2}\times84^\circ = 42^\circ$.

Answer:

$42^\circ$