We will to use the formula to a sector areaa, which is given for:
[tex]A=r^2\theta/2[/tex]
Where r is the radius and θ is the central angle.
We can rewrite the formula to obtain the central angle like this:
[tex]\theta=\frac{2A}{r^2}[/tex]
We replace with the values of the track:
[tex]\theta=\frac{2\ast51\pi}{20\ast3^2}=\frac{17\pi}{30}[/tex]
Then we change radians to degrees:
[tex]\frac{17\pi}{30}\ast\frac{180}{\pi}=102\text{ \degree}[/tex]
Then the correct answer is 102°.
