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