Question

In the given figure, express a in terms of b.

Answer 1

In Δ ABC,

BC = BA

∴ ∠BCA = ∠BAC
and Ext. ∠CBE = ∠BCA + ∠BAC

⇒ a = ∠BCA + ∠BCA

⇒ a = 2 ∠BCA .........(i)

But ∠ACB = 180° − b ..........(∵ ∠ACD and ∠ACB are linear pair)

⇒ ∠BCA = 180° − b .............(ii)

∴ a = 2 ∠BCA = 2 (180° − b)

= 360°− 2b