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In the given figure, $\overline{P Q}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle R O S=80^{\circ}$. When $\overline{P R}$ and $\overline{Q S}$ are extended, they meet at $T$. The value of $\angle R T S$ is $\_\_\_\_$

  1. $40^{\circ}$
  2. $50^{\circ}$
  3. $60^{\circ}$
  4. $80^{\circ}$

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