For the \( \text{NO}_2 \) ion, we consider the electron configuration based on the Lewis structure. The total number of electrons in \( \text{NO}_2^- \) is the sum of the electrons from nitrogen and oxygen atoms. Nitrogen has 5 valence electrons and each oxygen has 6 valence electrons. The negative charge adds an additional electron.
The total number of valence electrons is:
\[
5 \, (\text{from N}) + 6 \times 2 \, (\text{from 2 O}) + 1 \, (\text{from the negative charge}) = 18 \, \text{electrons}
\]
In the Lewis structure of \( \text{NO}_2^- \), 2 electrons are involved in the bonding between nitrogen and oxygen atoms, while the remaining electrons are non-bonded.
Thus, the number of non-bonded electrons is \( \boxed{12} \).