Step 1: Set up the moles.
Starting from one mole with degree of dissociation 0.20, the equilibrium moles are 0.80, 0.20 and 0.20.
Step 2: Partial pressures at 1 bar.
Divide each by the total of 1.20 to get the mole fractions and hence the partial pressures.
Step 3: Evaluate $K_p$.
\[ K_p = \frac{(0.20/1.20)^2}{0.80/1.20} = \frac{0.04}{0.96} = 0.083 \]
Step 4: Answer.
\[ \boxed{0.083} \]