Question

Based on the information given say whether or not △ABC∼△FED. Explain your reasoning. m∠A=70°, m∠B=x, m∠C=x+2°, m∠D=y, m∠E=y+5°, and m∠F=y+25°.

Answer 1

Answer: No, triangle ABC is not similar to triangle FED

Step-by-step explanation:

Here,   m∠A = 70°, m∠B = x, m∠C = x+2°

But, m∠A + m∠B + m∠C =180° ( By the property of a triangle)

⇒ 70+ x + x + 2 = 180

⇒ 2x + 72 = 180

⇒ 2x = 180 - 72  

⇒ 2x = 108

⇒ x = 54                

Thus,  m∠A = 70°, m∠B = 54°,  m∠C = 56°

Now In triangle FED, m∠D=y, m∠E=y+5°, and m∠F=y+25°.

But, m∠D + m∠E + m∠F = 180°

⇒ y + y + 5 + y + 25 = 180  

⇒ 3y + 30 = 180    

⇒ 3y = 150            

⇒ y = 50              

Thus, m∠D = 50°, m∠E = 55°, and m∠F = 75°

Also, m∠A ≠ m∠F, m∠B ≠ m∠E and m∠C ≠ m∠D

Thus, By the property of similarity,

Δ ABC and Δ FED are not similar.