CAT 2016 Quantitative Ability

In ΔABC, AB = AC
Let ∠ABC = ∠ACB=x°
and ∠BAC = y°
∴ 2x + y = 180°
In ∠FDE, ∠FED=x°
and ∠FDE = x - 30° (∵ DE||BC)
⇒ x+x-30 + 70 = 180°
∴ x = 70°
We see that ∠FED = ∠DFE
Hence, DEF is an isosceles triangle i.e. DE=DE = 4 cm.