What is the Lewis electron dot formula (Lewis structure) of nitrous oxide $ (N{{O}_{2}}) $ ?

Hint :To find the structure of molecules we must know the electronic configuration of the atoms that molecules possess. Valence electrons are used in making the structure of molecules. Valence electrons are the electrons that are present in the outermost shell of an atom.

Complete Step By Step Answer:
In this question, we have to find the most stable structure of $ N{{O}_{2}} $ . The structure will be stable if there will be a negative charge on more electronegative elements. Among nitrogen and oxygen, oxygen is more electronegative than nitrogen so the structure in which there will be a negative charge on nitrogen will be most stable.
Since the left nitrogen "owns" five valence electrons (two lone pairs and one from the $ N-O~ $ bond), and it expects five, its formal charge. Among given conditions the only option in which there is a negative charge on oxygen (usually it makes two bonds but there is only one bond) and a positive charge on the central nitrogen atom (usually nitrogen forms three bonds but central nitrogen has four bonds one with oxygen and three with another nitrogen atom). Charges on the structure will look like and the Lewis structure is given by;
 $ {{\left[ :\underset{\scriptscriptstyle\centerdot\centerdot}{\ddot{O}}:\dot{N}::\underset{\scriptscriptstyle\centerdot\centerdot}{\ddot{O}} \right]}^{{}}} $.

Additional Information:
 $ N{{O}_{2}} $ is nitrogen dioxide. It is one of the oxides of nitrogen. It is an intermediate formed during the synthesis of nitric acid. It is widely used in the production of fertilizers. $ N{{O}_{2}} $ is among primary pollutants. Pollutants are the substances which cause pollution.

Note :
Remember that the resonance structures are sets of Lewis structures. These structures describe the delocalization of electrons in an ion or a molecule. These structures are also called canonical structures.