Find the degree measure of the angle subtended at the centre of a circle of

Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$

$\theta=\frac{1}{r}$ where $\theta$ is central angle, $l=$ length of arc, $r=$ radius

Now,

$\theta=\frac{1}{r}$ and $r=0.5 \times$ diameter

$=\frac{16.5}{30}$ radians

$\theta$ in degrees $=\frac{16.5}{30} \times \frac{180}{\pi}=\frac{16.5}{30} \times \frac{180}{22 / 7}=\frac{16.5}{30} \times \frac{180 \times 7}{22}=\frac{20790}{660}=31.5^{\circ}$

$\theta$ in minutes $=0.5 \times 60=30^{\prime}$

Therefore angle subtended at the center is $31^{\circ} 30^{\prime}$