Based on the information given say whether or not △abc∼△fed. explain your reasoning.
m∠a=m∠b, m∠c=m∠a+30°, m∠e=m∠f=x, m∠d=2x−20°.

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F =

m∠D = °.

Now, let m∠A = m∠B =

So, m∠C = m∠A + 30° =

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.