In the given figure, \(\overline{PQ}\) is the diameter of a circle with center \(O\). Two points \(R\) and \(S\) are chosen on the circle such that \(\angle ROS = 80^\circ\). When \(\overline{PR}\) and \(\overline{QS}\) are extended, they meet at \(T\).
The value of \(\angle RTS\) is ______