(N/A) The formula for formal charge $(FC)$ is: $FC = \text{Total valence electrons} - \text{Total non-bonding electrons} - \frac{1}{2} \times \text{Total bonding electrons}$.
For the structure $:N=N=O:$,the atoms are labeled as $N_1$ (terminal),$N_2$ (central),and $O$ (terminal).
$1$. For $N_1$ (terminal nitrogen): Valence electrons = $5$,non-bonding electrons = $4$,bonding electrons = $4$. $FC = 5 - 4 - (4/2) = 5 - 4 - 2 = -1$.
$2$. For $N_2$ (central nitrogen): Valence electrons = $5$,non-bonding electrons = $0$,bonding electrons = $8$. $FC = 5 - 0 - (8/2) = 5 - 4 = +1$.
$3$. For $O$ (terminal oxygen): Valence electrons = $6$,non-bonding electrons = $4$,bonding electrons = $4$. $FC = 6 - 4 - (4/2) = 6 - 4 - 2 = 0$.
Thus,the formal charges are $N_1 = -1$,$N_2 = +1$,and $O = 0$.