Question

abc is an isoscale triangle in which ab =ac side ba is produced to d such that ad =ab show that bcd is a right angle

Answer 1

this is the right way to prove

Answer 2

∠b=∠acb=∠1
2∠1=∠dac
let ∠dac=∠4
and,
∠d=∠acd=∠2
2∠2=∠bac
let∠bac=∠3
in Δabc.
∠3+2∠1=180°
2∠2+2∠1=180°
∠1+∠2=90°           
inΔdac,
∠4+2∠2=180°
2∠1+2∠2=180°
∠1+∠2=90°

∠bcd=∠1+∠2=90°
∴∠bcd=90°
also,∠bcd is a right angle.

i think it help you 

THANK YOU :)  :)