A student makes the following two statements about quadrilaterals:
Statement I: If one pair of opposite angles of a quadrilateral sum to 180∘, then the quadrilateral is cyclic.
Statement II: If the other pair of opposite angles of the same quadrilateral do not sum to 180∘, then the quadrilateral cannot be cyclic.
(i) Examine Statement I and give a reasoned explanation as to whether it is always true.
(ii) Examine Statement II and justify whether it must be true, might be true, or is definitely false.
(iii) On the basis of your answers, state the exact condition on opposite angles that guarantees a quadrilateral is cyclic.