Question

applying the inscribed angle theorem
what is the measure of \\(\overarc{qs}\\)?

Explanation:

Step1: Recall the Inscribed Angle Theorem

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

Step2: Apply the theorem

Let the measure of arc \(QS\) be \(x\). The inscribed angle \(\angle QPS = 84^{\circ}\). According to the inscribed - angle theorem, \(\angle QPS=\frac{1}{2}\text{measure of arc }QS\). 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 \(x = 2\times84^{\circ}=168^{\circ}\).

Answer:

\(168^{\circ}\)