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Cyclic Quadrilateral

In the given ...

Question

In the given figure, $C D E F$ is a cyclic quadrilateral, $D E$ and $C F$ are produced to $A$ and $B$ respectively such that $A B ∥ C D$ . If $∠ F E D = 80^{\circ}$ , find $∠ F B A$ .

30^{\circ}

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60^{\circ}

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80^{\circ}

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10^{\circ}

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Solution

The correct option is C $80^{\circ}$
$C D E F i s a c y c l i c q u a d r i l a t e r a l . ∠ F E D = 80^{o} (G i v e n) ∠ F E D + ∠ F C D = 180^{o} . . . (s u m o f o p p o s i t e a n g l e s o f c y c l i c q u a d r i l a t e r a l i s 180^{o}) \Rightarrow F C D = 180^{o} - 80^{o} = 100^{o} . S i n c e A B ∥ C D, \Rightarrow A B C D i s a p a r a l l e l o g r a m . ∠ A B C + ∠ B C D = 180^{o} . . . (A d j a c e n t a n g l e s o f p a r a l l e l o g r a m . a r e s u p p l e m e n t a r y) ∠ B C D = ∠ F C D = 100^{o} \Rightarrow ∠ A B C = 180^{o} - 100^{o} = 80^{o} ∠ A B C = ∠ F B A = 80^{o} . H e n c e, o p t i o n C i s c o r r e c t .$

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Similar questions

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that $∠ A D C = 95^{\circ} a n d ∠ E C F = 20^{\circ} T h e n, ∠ B A D = ?$ .

(a) $95^{\circ}$

(b) $85^{\circ}$

(d) $75^{\circ}$

In the given figure, sides AB and CD of the quadrilateral ABCD are produced. Find the value of $x$.

A B C D

is a cyclic quadrilateral such that

∠ A D B = 30^{o}

and

∠ D C A = 80^{o}

, then

∠ D A B =

Q. In figure,

P A R S

is cyclic quadrilateral whose diagonal intersect at

A

∠ S Q R = 80^{0}

and

∠ Q P R = 30^{0}

, then find

∠ S R Q

Q. Construct a cyclic quadrilateral

A B C D

such that

A B = 6 c m, ∠ A = 60^{\circ}, ∠ A B D = 30^{\circ}

and

∠ C B D = 20^{\circ}

. Then,

l (C D) = ?

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In the given figure, CDEF is a cyclic quadrilateral, DEandCF are produced to AandB respectively such that AB∥CD. If ∠FED=80∘, find ∠FBA.

In the given figure, $C D E F$ is a cyclic quadrilateral, $D E$ and $C F$ are produced to $A$ and $B$ respectively such that $A B ∥ C D$ . If $∠ F E D = 80^{\circ}$ , find $∠ F B A$ .