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In the given figure, ABCD is a cyclic qu...

In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn paralllel to CD and BA is produced to F. If `angleABC =70^@` and `angleFAE=30^@`, Find `angleBCD`.

Text Solution

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If we extend `EA` to `G` as shown in figure, then,
`/_BAG = /_FAE = 30^@`
Also, we know, sum of opposite angles of a cyclic quadrilteral is `180^@`. `:. /_ADC+/_ABC = 180^@`
`=>/_ADC+70^@ = 180^@ =>/_ADC = 110^@`
As, `CD and GE` are parallel,
`:. /_CDA+/_DAG = 180^@`
`=>/_CDA+/_BAG+/_BAC = 180^@`
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