CAT 2000 — QA Question 47

Consider the given figure,

Let ∠DAE = x
In ΔABC, AB = BC
∴ m∠ACB =  m∠BAC = x
∴ Being an exterior angle of ΔABC, m∠CBF = 2x

In ΔAGF, FG = GA
∴ m∠AFG =  m∠GAF = x
∴ Being an exterior angle of ΔAGF, m∠CGF = 2x

In ΔBCD, BC = CD
∴ m∠CBD = m∠CDB = 2x
∴ Being an exterior angle of ΔACD, m∠DCE = 3x
∵ DE = CD, in ΔDCE, m∠CED = m∠ECD = 3x

In ΔGFE, EF = FG
∴ m∠FGE = m∠FEG = 2x
∴ Being an exterior angle of ΔAFE, m∠EFD = 3x
∵ DE = EF, in ΔDFE, m∠EFD = m∠EDF = 3x

In ΔADE,
x + 3x + 3x = 7x = 180°
∴ x ≡ 25°
∴ m∠DAE ≡ 25°

Hence, option (d).