Question

In Fig. ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. 

Find the values of x and y.

Answer 1

We have, 

∠BAD = 78° 

∠DCF = x° 

∠DEF = y° 

Since, 

ABCD is a cyclic quadrilateral 

∠BAD + ∠BCD = 180° 

78° + ∠BCD = 180° 

∠BCD = 102° 

Now, 

∠BCD + ∠DCF = 180° 

(Linear pair) 

102° = x – 180° 

x = 78° 

Since, 

DCEF is a cyclic quadrilateral 

x + y = 180° 

78° + y = 180° 

y = 102°