Question

question 3 of 10 what is the measure of ∠rst? a. 47° b. 77° c. 62° d. 124°

Explanation:

Step1: Recall angle - arc relationship

The measure of an inscribed angle is half the measure of its intercepted arc. The measure of $\angle RST$ is half of the sum of the measures of arcs $\overset{\frown}{PQ}$ and $\overset{\frown}{RT}$.

Step2: Calculate the sum of arcs

The sum of the measures of arcs $\overset{\frown}{PQ}$ and $\overset{\frown}{RT}$ is $47^{\circ}+77^{\circ}=124^{\circ}$.

Step3: Find the measure of $\angle RST$

Since $\angle RST$ is an inscribed - angle, $m\angle RST=\frac{1}{2}(m\overset{\frown}{PQ} + m\overset{\frown}{RT})$. Substituting the sum of the arcs, we get $m\angle RST=\frac{1}{2}(124^{\circ}) = 62^{\circ}$.

Answer:

C. 62°