Answer
See the answer below.
Work Step by Step
In $NO_2^+$ the nitrogen makes two double bonds and has no lone electron pair, therefore it has a linear geometry and a bond angle of 180$^{\circ}$.
In $NO_2^-$ the nitrogen makes one double
and one single bond and has one lone electron pair, therefore it has a bent geometry from the trigonal planar archetype and a bond angle of 120$^{\circ}$.
