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Question
In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
Solution
In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
We have to find the value of x and y.
Since ,ABCD is a cyclic quadrilateral
So `angle A + angle BCD = 180°` (Opposite angle of a cyclic quadrilateral are supplementary)
` angle BCD = 180° - angle A ` ` ( ∠ A = 78°)`
`angle BCD = 180° - 78°`
`angle BCD = 102°` ..… (1)
`angle BCD + angleDCF = 180°`
`DCF = 180° - angle BCD `
x = 180° − 102°
= 78°
Now in cyclic quadrilateral DCFE
x + y = 180° (Opposite angles of a cyclic quadrilateral are supplementary)
y = 180° − 78°
= 102°
Hence, x = 78° and y = 102°
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