Question

ng the inscribed angle theorem
what is the measure of $overset{\frown}{qs}$?

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of arc $\overset{\frown}{QS}$ be $x$. The inscribed angle $\angle QRS = 84^{\circ}$, and it intercepts arc $\overset{\frown}{QS}$.

Step2: Apply the formula

We know that $\angle QRS=\frac{1}{2}\text{ measure of }\overset{\frown}{QS}$. So, $84^{\circ}=\frac{1}{2}x$.

Step3: Solve for $x$

Multiply both sides of the equation $84^{\circ}=\frac{1}{2}x$ by 2. We get $x = 168^{\circ}$.

Answer:

$168^{\circ}$