What is the oxidation state of chlorine in ClO2?

To complete this you have to keep in mind that, oxygen has an oxidation number of - 2 unless in molecules with a polyatomic ions. In addition, when the sum of oxidation compounds is zero is a neutral compound. For ClO2 the oxidation number of oxygen is - 2 then the oxydation number of the two atoms is - 4. Therefore the oxidation number of Cl is + 4. So we add them, 4 + (-2) + (-2) = 0 therefore it is a neutral compound.