Answer
$0.346^{\circ}$
Work Step by Step
First, we can use the given frequency, $f=220*10^9Hz$, and the speed of light to find the wavelength.
$\lambda = c / f$
$\lambda = (3.00*10^8m/s) / (220*10^9Hz)$
$\lambda =1.36*10^{-3}m$
Now we can use the given diameter of the antenna, $d=55.0*10^{-2}m$, in equation (36-12), to find the angle, $\theta$.
$\sin \theta= 1.22 \frac{\lambda}{d}$
$ \theta=\arcsin( 1.22 \frac{\lambda}{d})$
$ \theta=\arcsin( 1.22 \frac{1.36*10^{-3}m}{55.0*10^{-2}m})$
$\theta = .173^{\circ}$
They asked use for the angular width, $2\theta$, of the central maximum, from first minimum to first minimum.
So therefore: $2\theta=2* .173^{\circ}=0.346^{\circ}$
