what is m∠qsr? write your answer as an integer or decimal. m∠qsr =
what is m∠qsr? write your answer as an integer or decimal. m∠qsr =
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
Step2: Identify the central and inscribed angles
The central angle $\angle QPR = 89^{\circ}$, and the inscribed angle $\angle QSR$ subtends the same arc $\overset{\frown}{QR}$.
Step3: Calculate the measure of $\angle QSR$
By the inscribed - angle theorem, $m\angle QSR=\frac{1}{2}m\angle QPR$. Since $m\angle QPR = 89^{\circ}$, then $m\angle QSR=\frac{89}{2}=44.5^{\circ}$.
Answer:
$44.5$