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If ABC and DEF are similar triangles such that ∠A = 47° and ∠E = 83°, then ∠C =

A. 50° 

B. 60° 

C. 70° 

D. 80°

1 Answer

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Best answer

Given ABC and DEF are two similar triangles, ∠A = 47° and ∠E = 83°

We know that SAS similarity criterion states that if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

In ΔABC and ΔDEF,

if \(\frac{AB}{DE}\) = \(\frac{AC}{DF}\) and ∠A = ∠D, 

then ΔABC ~ ΔDEF

So, 

∠A = ∠D 

⇒ ∠D = 47° … (1) 

Similarly, ∠B = ∠E 

⇒ ∠B = 83° … (2) 

We know that the sum of all angles of a triangle is equal to 180°. 

⇒ ∠A + ∠B + ∠C = 180° 

⇒ 47° + 83° + ∠C = 180° 

⇒ 130° + ∠C = 180° 

⇒ ∠C = 180° - 130° = 50° 

∴ ∠C = 50°

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