What is the angle between the carbon-oxygen and carbon-nitrpgen bond in cyanate ion

Each cyanate ion [tex]\text{OCN}^{-}[/tex] contains one carbon atom, one oxygen atom, and one nitrogen atom. The ion carries a charge of negative one.

Each oxygen atom demands two extra electrons to form an octet.
Each nitrogen atom demands three extra electrons to form an octet.
Each carbon atom demands four extra electron to form an octet.
The negative charge indicates that one extra electron has already been added to the three atoms.

The ion would demand [tex]2 + 3 + 4 - 1 = 8[/tex] extra electrons to ensure a complete octet for each of its atom. It would do so by forming [tex]8/2 = 4[/tex] covalent bonds.

There are two possible configurations:

The extra electron might have ended up on the oxygen atom. There would be a carbon-oxygen single bond and a carbon-nitrogen triple bond.
The extra electron might have gone to the nitrogen atom. There would be double bonds between both carbon and oxygen and between carbon and nitrogen.

Either way, the central carbon atom would end up with two electron domains and no lone pairs. By the VSEPR theory, the molecule would end up with a linear geometry. It would thus have an O-C-N bond angle of 180 degrees.