In Fig. 16.187, BAD=78°, DCF=x° and DEF=y°. Find the values of x and y.

We have,

BAD = 78o


DCF = xo


DEF = yo


Since, ABCD is a cyclic quadrilateral


BAD + BCD = 180o


78o + BCD = 180o


BCD = 102o


Now,


BCD + DCF = 180o (Linear pair)


102o = x – 180o


x = 78o


Since,


DCEF is a cyclic quadrilateral


x + y = 180o


78o + y = 180o


y = 102o


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