In quadrilateral ABCD, the measures of two opposite angles are given by ∠A=3x+5∘ and ∠C=5x−25∘. The other two angles satisfy the relation ∠B:∠D=2:3.
(i) Determine the value of x for which ABCD can be a cyclic quadrilateral.
(ii) Using the value of x obtained in part (i), calculate ∠B and ∠D. Show all necessary steps.