A quadrilateral ABCD is drawn such that all four vertices lie on the circumference of a circle.
(i) State the theorem that relates the sum of a pair of opposite angles of a cyclic quadrilateral.
(ii) Draw a neat labelled sketch of the situation described above and mark the opposite angles.
(iii) Prove, with full reasoning, that ∠A+∠C=180∘ and ∠B+∠D=180∘ for the quadrilateral ABCD. Explain each step of your proof clearly, quoting the theorems you use.