Question

In ∆ ABC, BA and BC are produced. Find the angles a and h. if AB = BC.

Answer 1

In Δ ABC, sides BA and BC are produced
∠ABC = 54°; AB = BC

Now in Δ ABC,

∠BAC + ∠BCA + ∠ABC = 180° ...........(Angles of a triangle)

⇒ ∠BAC + ∠BAC + 54° = 180° .............(∵ AB = BC)

⇒ 2 ∠BAC = 180° − 54°

⇒ 2 ∠BAC = 126°

∴ ∠BAC =`(126°)/2=63°` and ∠BCA = 63°

∠BAC + b = 180° ..............(Linear pair)

⇒ 63° + b = 180°

⇒ b = 180° − 63° = 117°

and ∠BCA + a = 180° ............(Linear pair)

∴ 63° + a = 180°

⇒ a = 180° − 63° = 117°

Hence a = 117°, b = 117