We know that segment RS is a diameter of the circle, this means that arcs RS an RST measure 180°. Now that we know that an using the ratio for arcs RT and TS given we have:
[tex]\begin{gathered} RT+5RT=180 \\ 6RT=180 \\ RT=\frac{180}{6} \\ RT=30 \end{gathered}[/tex]
Now, we know that an angle inscribed in a circle is half its intercepted arc, then we have:
[tex]m\angle RST=\frac{30}{5}=15[/tex]
Therefore, we have that arc RT is 30° and angle RST is 15°
