The correct increasing order of the O-N-O bond angles in NO₂^+ , NO₂ and NO₂^- is :

Step-by-step solution

In NO₂^+ , the central nitrogen atom is sp hybridized with no lone pairs, resulting in a linear geometry and a bond angle of 180^ . In NO₂ , the nitrogen atom is sp^2 hybridized and possesses a single odd electron. The repulsion between the odd electron and the bond pairs is less than that of a full lone pair, resulting in a bond angle of approximately 134^ . In NO₂^- , the nitrogen atom is sp^2 hybridized and has one complete lone pair. The lone pair-bond pair repulsion is stronger than the odd electron-bond pair