In △ABC and △DEF, $$∠A=40^∘, ∠B=55^∘,∠D=55^∘,∠E=85^∘$$​ and m((AB) ̅)=m((FD) ̅). Then which of the options below is correct?

Correct option is D

Given:
 ΔABC and ΔDEF, ∠A = 40°, ∠B = 55°, ∠D = 55°, ∠E = 85° 

AB = FD  

Concept Used: 

Sum of interior angle of triangle = $$180\degree$$ 

Two triangles can be congruent by;

Angle - side - angle(ASA) property 

Side - angle - side (SAS) property

Side - side - side(SSS) property

Solution:

As per the question,

In the triangle DEF, we have:

∠F =180° - (∠D + ∠E)

= 180° - 140°
 = 40°
and ∠A = ∠F = 40°
And in triangle ABC, we have:
∠C = 180° - (40° + 55°)
 = 180° - 95°
 = 85°
Therefore, ∠C = ∠E = 85°

and AB =  FD

​Therefore, ∆ ABC ≅ ∆FDE (by ASA)

Thus, correct answer is Δ ABC ≅ Δ FDE

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