In equilateral triangle ΔDEF, X and Y are points on the side DE and DF respectively, such that DX = FY, EY and FX intersect at Z. The measure (in degrees) of ∠FZE is ?
Answer & explanation
Correct answer: option 2
ΔEFY ≅ ΔDFX [by SAS congruency]
So, the three angles of these two triangles are the same.
Let ∠YEF = θ ⇒ ∠DFX is also θ
Now ∠EYF = 180° - (60° + θ) = 120° - θ
Now, in ΔFYZ
Exterior angle ∠FZY = (120° + θ) + θ = 120°