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Question -

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.



Answer -

It is given that,  and ,   are cyclic quadrilateral
 
We have to find the value of x and y.
Since ,  is a cyclic quadrilateral
So       (Opposite angle of a cyclic quadrilateral are supplementary)
         ( )
 
       ..… (1)
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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