what is the measure of arc qr? 26° 52° 104° 128°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the inscribed angle and the intercepted arc

The inscribed angle $\angle QSR = 52^{\circ}$, and the intercepted arc is $\overset{\frown}{QR}$.

Step3: Calculate the measure of the arc

Let the measure of arc $\overset{\frown}{QR}$ be $x$. According to the inscribed - angle theorem, $\angle QSR=\frac{1}{2}\overset{\frown}{QR}$. So $x = 2\times\angle QSR$. Substitute $\angle QSR = 52^{\circ}$ into the formula: $x=2\times52^{\circ}=104^{\circ}$.

Answer:

$104^{\circ}$