Answer
$\theta = 0.01525~rad$
$\theta = 0.87^{\circ}$
Work Step by Step
We can find the angle of the first dark fringe:
$\theta = \frac{1.22~\lambda}{d}$
$\theta = \frac{(1.22)~(2.5\times 10^{-6}~m)}{0.20\times 10^{-3}~m}$
$\theta = 0.01525~rad$
We can convert this angle to degrees:
$\theta = (0.01525~rad)(\frac{180^{\circ}}{\pi~rad})$
$\theta = 0.87^{\circ}$
