If ABC and DEF are similar triangles such that ∠A = 57° and ∠E =

1.	If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C ?
Answer» 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°

If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C ?

Answer»

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°

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