Answer
$0.01$ rad $(0.573 ^\circ)$
Work Step by Step
Using the double-slit formula $dsin\theta = m\lambda$ and using $m=1$ for the first fringe yields $$dsin\theta=\lambda$$ Solving for $sin\theta$ yields $$sin\theta=\frac{\lambda}{d}$$ Therefore, by taking the arcsin of each side and using $d=100\lambda$, you get $$\theta=arcsin(\frac{\lambda}{100\lambda})=arcsin(\frac{1}{100})=0.01rad (0.573 ^\circ)$$
