Question

question 9 of 10 what is the measure of ∠rst?

Explanation:

Step1: Recall angle - arc relationship

The measure of an inscribed angle is half the measure of its intercepted arc. The measure of the arc $PT$ is $47^{\circ}+77^{\circ}=124^{\circ}$.

Step2: Calculate $\angle{RST}$

Since $\angle{RST}$ is an inscribed angle that intercepts arc $PT$, by the inscribed - angle theorem, $m\angle{RST}=\frac{1}{2}m\overset{\frown}{PT}$. So $m\angle{RST}=\frac{1}{2}\times124^{\circ}=62^{\circ}$.

Answer:

C. 62°