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