Question

Is ∆ABC right-angled at B?
I. ABCD is a cyclic quadrilateral.
II. ∠D = 90°.

(a) if the given question can be answered by any one of the statements but not the other;
(b) if the given question can be answered by using either statement alone;
(c) if the given question can be answered by using both the statements together but cannot be answered by using either statement;
(d) if the given question cannot be answered by using both the statements together.

Answer 1

(c) The given question can be answered by using both the statements together but cannot be answered by using either of the statements.
I gives ∠B + ∠D = 180° and ∠A + ∠C = 180°.
II gives ∠D = 90°.
∴ I and II together give ∠B = 90°.
Thus, the given question can be answered by using both statements.