Question

In Fig. ABCD is a cyclic quadrilateral. 

Find the value of x.

Answer 1

∠FDC + ∠CDA = 180° 

(Linear pair) 

80° + ∠CDA = 180° 

∠CDA = 100° 

Since, 

ABCD is a cyclic quadrilateral 

∠ADC + ∠ABC = 180° 

100° + ∠ABC = 180° 

∠ABC = 80° 

Now, 

∠ABC + ∠ABF = 180° 

(Linear pair) 

80° + x = 180° 

x = 180° – 80° 

= 100°