Question

In the given figure, ABCD and ABEF are two cyclic quadrilaterals. If ∠BCD = 110°, then ∠BEF = ?
(a) 55°
(b) 70°
(c) 90°
(d) 110°

Answer 1

(d) 110°
Since ABCD is a cyclic quadrilateral, we have:
∠BAD + ∠BCD = 180°
⇒ ∠BAD + 110° = 180°
⇒∠BAD = (180° - 110°) = 70°
Similarly in ABEF, we have:
∠BAD + ∠BEF = 180°
⇒ 70° + ∠BEF = 180°
⇒ ∠BEF = (180° - 70°) = 110°