Identify the coordination mode of $EDTA^{4-}$

$EDTA^{4-}$ is a hexadentate ligand. It binds to the metal ion through:

• $2$ nitrogen donor atoms
• $4$ oxygen donor atoms

So in $[Co(EDTA)]^-$, cobalt is 6-coordinate, giving an octahedral arrangement around Co.

Count possible $N-Co-O$ bond angles

We need the number of bond angles of the type $N-Co-O$.

Since there are:

• $2$ nitrogen atoms
• $4$ oxygen atoms

each nitrogen can form an angle at Co with each oxygen.

Therefore total number of distinct $N-Co-O$ angles is: $2 \times 4 = 8$

Why no further distinction is needed

In an octahedral complex, some such angles may be $90^\circ$ and some may be $180^\circ$, but the question asks for the total number of $N-Co-O$ bond angles, not only one specific value.

Hence we count all nitrogen–cobalt–oxygen combinations.

Final answer

$\boxed{8}$