(d ) Let the angle C be x. Then, ∠A = 2x Also. ∠B - ∠D =
2x
3
We know that opposite angles of a cyclic quadrilateral are supplementary i.e. ∠A + ∠C = 180° ⇒ 2x + x = 180° ⇒ 3x = 180° ⇒ x = 60° ∴ ∠A = 2x = 120° and ∠B - ∠D =
120°
3
= 40 .......(i) Also, ∠B + ∠D =180° ..........(ii) On solving Eqs (i) and (ii). we get ∠D = 70° and ∠B = 110° ∴ Maximum difference = 120° - 60° = 60°