Step 1: Understand the question.
We must pick the halogen oxide used to measure carbon monoxide ($CO$) in a gas sample.
Step 2: Recall the property of CO.
Carbon monoxide is a strong reducing agent. So we need an oxide that can oxidise it cleanly and completely.
Step 3: Look at the choices.
$Cl_2O_7$, $BrO_3$ and $I_2O_7$ are not the standard reagents for this. The known reagent is iodine pentoxide, $I_2O_5$.
Step 4: Write the key reaction.
Iodine pentoxide oxidises CO to carbon dioxide and is itself reduced to iodine. \[ I_2O_5 + 5CO \rightarrow I_2 + 5CO_2 \]
Step 5: See how the measurement works.
The iodine set free is measured. Its amount tells us exactly how much CO was present, because they are in a fixed ratio.
Step 6: Choose the right oxide.
The oxide that does this job is $I_2O_5$.
Step 7: State the final answer.
The halogen oxide used is:
\[ \boxed{I_2O_5} \]