2. For the propositions

I. A cyclic pentagon with equal interior angles is a regular pentagon.
II. A cyclic quadrilateral with equal interior angles is a regular quadrilateral, which of the following conclusions is correct?
(A) Both I and II are correct;
(B) I is correct, II is incorrect;
(C) I is incorrect, II is correct;
(D) Both I and II are incorrect.
2. (B)

Proposition I is correct, the proof is as follows:
In the figure, $A B C D E$ is a cyclic pentagon with all interior angles equal. From $\angle A=\angle B$, we know $\overparen{B C E}=\overparen{C E A}$, thus $\overparen{B C}=\overparen{E A}$.
$$
\therefore B C=E A \text {. }
$$

Similarly, we can prove $B C=D E=A B=C D=E A$. Therefore, $A B C D E$ is a regular pentagon.

Proposition $\mathbb{I}$ is not correct, a counterexample is as follows: In the figure, $A B C D$ is a cyclic rectangle, $\angle A=\angle B=\angle C=\angle D=90^{\circ}, A B=C D, B C=D A$, but $A B \neq B C$. Clearly, $A B C D$ satisfies the conditions of Proposition $\mathbb{I}$, but is not a regular quadrilateral.