In the given figure, ABCD and ABEF are two cyclic quadrilaterals.
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°

 

Solution:

(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°

 

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