The type of hybrid orbitals used by chlorine atom in ${\mathrm{ClO}}_2$ is

The type of hybrid orbitals used by chlorine atom in ${\mathrm{ClO}}_2$ is ${\mathrm{sp}}^3$.

There are four unpaired electrons around Cl in ${\mathrm{ClO}}^{2-}$. Hence, Cl involves ${\mathrm{sp}}^3$ hybrid orbitals.

Hence, option A is correct.