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What will be the value of $∠ B C D$ , if in the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, E is produced with $∠ A B C = 920$ and $∠ F A E = 200$ ?

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108 ∘

104 ∘

102 ∘

100 ∘

answer is A.

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Detailed Solution

It is given that ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, E is produced with

∠ A B C = 920

and

∠ F A E = 200

We have to find the

∠ B C D

.
We know that in a cyclic quadrilateral, the opposite pairs of angles are supplementary. And, the exterior angle of the cyclic quadrilateral is equal to the opposite interior angle.
We know, AE||CD.
So, the value of

∠ A D C

∠ A B C + ∠ A D C = 1800 ⇒ 920 + ∠ A D C = 1800 ⇒ ∠ A D C = 880

Now the value of

∠ E A D

and

∠ B C D

:
Since, AE||CD

∠ E A D = ∠ A D C ∴ ∠ E A D = 880

∠ B C D = ∠ D A F ⇒ ∠ B C D = ∠ D A E + ∠ E A F ⇒ ∠ B C D = 880 + 200 = 1080

So, the value of

∠ B C D = 1080

.
Therefore, option 1 is correct.

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