[tex]x=20^{\circ}[/tex]
1) In this problem, we can see two Secant lines coming from a point outside the circle.
2) Let's sketch this out to better grasp how to deal with that:
From this situation, we can write out the following relation:
[tex]\begin{gathered} m\angle PRT=\frac{1}{2}(mRT-mQR) \\ \end{gathered}[/tex]
So, we can plug into that the given data, the measure of the angle and the measure of the arcs:
[tex]\begin{gathered} m\angle PRT=\frac{1}{2}(mRT-mQR) \\ 60^{\circ}=\frac{1}{2}(8x-2x) \\ 60^{\circ}=4x-x \\ 3x=60^{\circ} \\ \frac{3x}{3}=\frac{60^{\circ}}{3} \\ x=20^{\circ} \end{gathered}[/tex]
Hence, after solving that for x, we can state the answer is:
[tex]x=20^{\circ}[/tex]
