Question

practice with inscribed angle theorems and corollaries and the angle formed by a tangent and chord theorem. what is the measure of $widehat{qs}$?

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Calculate the arc measure

Let the measure of $\overset{\frown}{QS}$ be $x$. According to the inscribed - angle theorem, $\angle QRS=\frac{1}{2}\overset{\frown}{QS}$. So, $x = 2\times\angle QRS$.
$x=2\times84^{\circ}$

Answer:

$168^{\circ}$