Question

In the given figure, ABCD and ABEF are two cyclic quadrilateral. If $\angle BCD={110}^{\circ }then\angle BEF=?$

(a) ${55}^{\circ }$

(b) ${70}^{\circ }$

(c) ${90}^{\circ }$

(d) ${110}^{\circ }$

Answer 1

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