Question

ABCD is a cyclic quadrilateral in which ab parallel to CD if side CD is produced to both sides and Angle A D Q =80 then find Angle BCP​

Answer 1

Answer:

ABCD is a cyclic quadrilateral and AB and CD are produced to meet at E.

We know that opposite angles of a cyclic quadrilateral are supplementary.

∴  ∠BAD+∠BCD=180o           ------ ( 1 )

and ∠BAD+∠EAD=180o               ----- ( 2 )

From equation ( 1 ) and ( 2 ), we get,

∠BAD+∠EAD=∠BAD+∠BCD

∴  ∠EAD=∠BCD           --- ( 3 )

Similarly,

⇒  ∠ABC+∠ADC=180o       ---- ( 4 )

and ∠ADC+∠ADE=180o             ----- ( 5 )

From equation ( 4 ) and ( 5 ), we get

⇒ ∠ADC+∠ADE=∠ADC+∠ABC

⇒  ∠ADE=∠ABC                ----- ( 6 )

And ∠AED=∠BEC        [ Common angle ]      ---- ( 7 )

∴  From equation ( 3 ), ( 6 ) and ( 7 ), △EBC and △EDA are equiangular.



Answer 2

Answer:

80 I think it is correct because I have guessed the answer without seeing question