ΔABC and ΔDEF are two triangles such that ΔABC ≅ ΔFDE. If AB=17 cm, ∠B=52° and ∠A=95°, then which of the following options is true?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. DF=17 cm,∠E=33°.
According to the question, ΔABC ≅ ΔFDE
Then, AB = DF, BC = DE, and CA = EF
So, AB = DF = 17 cm
Also, ∠A = ∠F = 95° and ∠B = ∠D = 52°
∠C = ∠E
The sum of the three angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
⇒ 95° + 52° + ∠C = 180°
⇒ ∠C = 180° - 95° - 52° = 33°
⇒ ∠E = 33°
Therefore, DF = 17 cm and ∠E = 33°.