Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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 $∠ F A E = 200$ ?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

108 ∘

104 ∘

102 ∘

100 ∘

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!