Question

question 7 of 10
what is the measure of ∠rst?
a. 62°
b. 124°
c. 77°
d. 47°

Explanation:

Step1: Recall inscribed - angle formula

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

Step2: Find the sum of the arcs

The sum of the arcs of a circle is $360^{\circ}$. Let the arc $PR = x$ and arc $QT=y$. We know that one arc is $47^{\circ}$ and another is $77^{\circ}$. The sum of the two given arcs is $47^{\circ}+77^{\circ}=124^{\circ}$.

Step3: Calculate the measure of $\angle{RST}$

The measure of $\angle{RST}$ is half of the sum of the arcs it intercepts. The sum of the arcs it intercepts is $124^{\circ}$, so $\angle{RST}=\frac{1}{2}(47^{\circ} + 77^{\circ})=\frac{124^{\circ}}{2}=62^{\circ}$.

Answer:

A. $62^{\circ}$