In circle $Q, Q R=4$ and the length of $R S=2 \pi$. Find $\mathrm{m} \angle R Q S$.
Answer: $\mathrm{m} \angle R Q S=$

Step 1 ：Given the radius of the circle, QR, and the length of the arc RS, we need to find the measure of the angle RQS.

Step 2 ：We know that the length of an arc is given by the formula: \(Arc\,length = radius \times angle\,(in\,radians)\)

Step 3 ：In this case, we have: \(Arc\,length\,(RS) = 2\pi\) and \(Radius\,(QR) = 4\)

Step 4 ：We can rearrange the formula to find the angle in radians: \(Angle\,(in\,radians) = \frac{Arc\,length}{Radius}\)

Step 5 ：\(Angle\,(in\,radians) = \frac{2\pi}{4} = \frac{\pi}{2}\)

Step 6 ：Convert the angle from radians to degrees: \(Angle\,(in\,degrees) = \frac{180}{\pi} \times \frac{\pi}{2} = 90\)

Step 7 ：\(\boxed{\mathrm{m}\,\angle\,RQS = 90\,degrees}\)