SOLUTION
To calculate the value of x the length of arc formula will be used
The formua for length of arc is
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]
From the given circle
L= 14
r=27
Substitute the values into the formula
[tex]14=\frac{x}{360}\times2\pi\times27[/tex]
Solve for x
[tex]\begin{gathered} 14\times360=54\pi x \\ 5040=54\pi x \\ x=\frac{5040}{54\pi} \end{gathered}[/tex]
Hence the value of x is
[tex]x=29.7^{\circ}[/tex]
Therefore the required angle is 29.7⁰
