Answer
Statements I and II contradict each other.
Work Step by Step
In a right triangle, one of the angles must measure $90^{\circ}$. This means that both $\angle A$ and $\angle C$ cannot be $60$; they would have to be $45^{\circ}$ each if the third angle has to be $90^{\circ}$. Therefore, statements I and II contradict each other.
