Question

question 4 of 10 what is the measure of ∠rst? a. 47° b. 62° c. 124° d. 77°

Explanation:

Step1: Recall inscribed - angle formula

The measure of an inscribed angle is half the measure of its intercepted arc. The sum of the arcs of a circle is 360°. Let the arc $PR$ be $x$ and arc $QT$ be $y$. We know that the measure of an inscribed - angle $\angle RST$ is related to the arcs it intercepts. The formula for the measure of an inscribed angle $\theta$ is $\theta=\frac{1}{2}(m\overset{\frown}{PR}+m\overset{\frown}{QT})$. First, find the sum of the given arcs: $47^{\circ}+77^{\circ} = 124^{\circ}$.

Step2: Calculate the measure of $\angle RST$

Since $\angle RST$ is an inscribed angle and the sum of the arcs it intercepts is $124^{\circ}$, using the formula $\angle RST=\frac{1}{2}(m\overset{\frown}{PR}+m\overset{\frown}{QT})$, we have $\angle RST = 62^{\circ}$.

Answer:

B. $62^{\circ}$