Question

in circle q with ( mangle psr = 39^{circ} ), find the measure of minor arc ( overparen{pr} ).

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the arc it intercepts.

Step2: Apply the theorem

Given that $\angle PSR$ is an inscribed angle and it intercepts arc $\overset{\frown}{PR}$. Let $m\overset{\frown}{PR}=x$. According to the inscribed - angle theorem, $m\angle PSR=\frac{1}{2}m\overset{\frown}{PR}$.

Step3: Solve for the arc measure

Since $m\angle PSR = 39^{\circ}$, we have $39^{\circ}=\frac{1}{2}x$. Multiply both sides of the equation by $2$: $x = 2\times39^{\circ}=78^{\circ}$.

So, the measure of minor arc $\overset{\frown}{PR}$ is $78^{\circ}$.

Answer:

$78^{\circ}$