Given
ABC and DEF are two similar triangles, ∠A = 57° and ∠E = 73°
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 = 57° … (1)
Similarly, ∠B = ∠E
⇒ ∠B = 73° … (2)
We know that the sum of all angles of a triangle is equal to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 57° + 73° + ∠C = 180°
⇒ 130° + ∠C = 180°
⇒ ∠C = 180° - 130° = 50°
∴ ∠C = 50°
