In the given figure, ABCD is a cyclic quadrilateral in which AE is dra

1.	In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 92° and ∠FAE = 20°, find ∠BCD.
Answer» We know that ABCD is a cyclic quadrilateral So we get ∠ABC + ∠ADC = 180^o By substituting the values 92^o + ∠ADC = 180^o On further calculation ∠ADC = 180^o – 92^o By subtraction ∠ADC = 88^o We know that AE \|\| CD From the figure we know that ∠EAD = ∠ADC = 88^o We know that the exterior angle of a cyclic quadrilateral = interior opposite angle So we get ∠BCD = ∠DAF We know that ∠BCD = ∠EAD + ∠EAF It is given that ∠FAE = 20^o By substituting the values ∠BCD = 88^o + 20^o By addition ∠BCD = 108^o Therefore, ∠BCD = 108^o.

In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 92° and ∠FAE = 20°, find ∠BCD.

Answer»

We know that ABCD is a cyclic quadrilateral

So we get

∠ABC + ∠ADC = 180^o

By substituting the values

92^o + ∠ADC = 180^o

On further calculation

∠ADC = 180^o – 92^o

By subtraction

∠ADC = 88^o

We know that AE || CD

From the figure we know that

∠EAD = ∠ADC = 88^o

We know that the exterior angle of a cyclic quadrilateral = interior opposite angle

So we get

∠BCD = ∠DAF

We know that

∠BCD = ∠EAD + ∠EAF

It is given that ∠FAE = 20^o

By substituting the values

∠BCD = 88^o + 20^o

By addition

∠BCD = 108^o

Therefore, ∠BCD = 108^o.

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