To find the length of arc, we can use the formula
[tex]l=\frac{\theta}{360}\times2\pi r[/tex]
The radius (r) is half of PS, hence
[tex]\begin{gathered} r=\frac{28}{2} \\ r=14\text{ f}eet \end{gathered}[/tex]
To find the angle:
[tex]\begin{gathered} \angle QXR=125-97\text{ (vertically opposite angles are equal)} \\ \angle QXR=28^{\circ} \end{gathered}[/tex]
The Sum of angles in a point will give us
[tex]\begin{gathered} \angle QXR+\angle RXS+\angle SXT+\angle TXP+\angle QXP=360_{} \\ \text{But} \\ \angle QXP=\angle SXT\text{ (Vertically opposite angles are equal)} \\ \text{Therefore} \\ 28+97+\angle QXP+125+\angle QXP=360 \end{gathered}[/tex]
Collecting like terms, we have
[tex]\begin{gathered} 2\angle QXP=360-97-28-125 \\ =110 \\ \angle QXP=\frac{110}{2}=55^{\circ} \end{gathered}[/tex]
Therefore, the angle of arc RPT can be given as
[tex]\begin{gathered} \angle QXR+\angle QXP+\angle PXT \\ \theta=28+55+125=208^{\circ} \end{gathered}[/tex]
Therefore, we find the length of the arc given we have all the parameters needed.
Hence,
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ =\frac{208}{360}\times2\times\pi\times14 \\ l=50.8\text{ fe}et \end{gathered}[/tex]
Therefore, the length of the arc RPT is 50.8 feet to the nearest tenth.
