what is m∠prq? write your answer as an integer or decimal. m∠prq = °
what is m∠prq? write your answer as an integer or decimal. m∠prq = °
Answer
Explanation:
Step1: Find the central - angle corresponding to arc PQ
The sum of angles around a point is 360°. The central - angle $\angle PSQ=360-(106 + 123)=360 - 229=131^{\circ}$.
Step2: Use the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Here, $\angle PRQ$ is an inscribed angle and $\angle PSQ$ is the central angle subtended by arc $PQ$. So, $m\angle PRQ=\frac{1}{2}m\angle PSQ$.
Step3: Calculate the measure of $\angle PRQ$
$m\angle PRQ=\frac{1}{2}\times131 = 65.5^{\circ}$
Answer:
$65.5$