Step 1: Recall oxidation state of potassium.
Potassium is an alkali metal and belongs to Group 1.
It generally shows a fixed oxidation state of \( +1 \) in its compounds.
Step 2: Oxidation number in \( K_2O \).
In \( K_2O \), oxygen has oxidation number \( -2 \).
Let oxidation number of potassium be \( x \).
\[
2x + (-2) = 0
\]
\[
2x = 2
\]
\[
x = +1
\]
Step 3: Oxidation number in \( K_2O_2 \).
In \( K_2O_2 \), oxygen is present as peroxide ion \( O_2^{2-} \).
The total charge on peroxide ion is \( -2 \).
Let oxidation number of potassium be \( x \).
\[
2x + (-2) = 0
\]
\[
2x = 2
\]
\[
x = +1
\]
Step 4: Oxidation number in \( KO_2 \).
In \( KO_2 \), oxygen is present as superoxide ion \( O_2^- \).
The total charge on superoxide ion is \( -1 \).
Let oxidation number of potassium be \( x \).
\[
x + (-1) = 0
\]
\[
x = +1
\]
Step 5: Conclusion.
Thus, the oxidation number of potassium in \( K_2O \), \( K_2O_2 \), and \( KO_2 \) is \( +1 \) in each case.
Therefore:
\[
\boxed{+1,\; +1,\; +1}
\]