(iv) In the adjoining figure, ABCD is a cyclic quadrilateral. BA is extended to the point F. IfAE||CD, <ABC = 92º and <FAE =20°, then the value of <BCD is
(a) 20° (b) 889
(c) 1089
(d) 720
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Step-by-step explanation:
Given,
In cyclic quad. ABCD
AF∣∣CB and DA is produced to E such that ∠ADC=92
∘
and ∠FAE=20
∘
So,
∠B+∠D=180
∘
∠B+92
∘
=180
∘
∠B=88
∘
As AF∣∣CB, ∠FAB=∠B=88
∘
But, ∠FAD=20
∘
[Given]
Ext. ∠BAE=∠BAF+∠FAE
=88
∘
+22
∘
=108
∘
But, Ext. ∠BAE=∠BCD
Therefore,
∠BCD=108
∘
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