Question

In the given figure, ABCD is a cyclic quadrilateral. AF is drawn parallel to CB and DA is produced to point E. If ∠ADC = 92°, ∠FAE = 20°; determine ∠BCD. Give reason in support of your answer.

Answer 1

In cyclic quad. ABCD,

AF || CB and DA is produced to E such that ∠ADC = 92° and ∠FAE = 20°

Now, we need to find the measure of ∠BCD

In cyclic quad. ABCD,

`=>` ∠B + ∠D = 180°

`=>` ∠B + 92° = 180°

`=>` ∠B = 180° – 92°

`=>` ∠B = 88°

Since AF || CB, ∠FAB = ∠B = 88°

But, ∠FAE = 20°   ...[Given]

Ext. ∠BAE = ∠BAF + ∠FAE

= 88° + 20° 

= 108°

But, Ext. ∠BAE = ∠BCD

∴ ∠BCD = 108°