Given:
The perimeter is 19 cm.
Acr length is 9 cm.
The perimeter of circle is calculated as,
[tex]\begin{gathered} \text{Perimeter POQ=PO+OQ+length of PQ} \\ 19=r+r+9 \\ 10=2r \\ r=5 \end{gathered}[/tex]
The arc length is calculated as,
[tex]\begin{gathered} \text{Arc length =}\theta\times\frac{\pi}{180}\times r \\ 9=\theta\times\frac{\pi}{180}\times5 \\ 9=\theta\times\frac{\pi}{36} \\ \theta=103.13 \\ \theta\approx103^{\circ} \end{gathered}[/tex]
Answer:
[tex]\theta=103^{\circ}[/tex]
