how would you solve : ( ?

Question

Given ?ABC ~ ?DEF,  m<A=46°  ,  

and  m< 39° how do you find m<f ???

Answer 1

If you have similar triangles, then the corresponding angles are identical.

 

This means, if ΔABC is similar to ΔDEF, then 

1. ∠A = ∠D
2. ∠B = ∠E
3. ∠C = ∠F

I recommend you draw the triangles to help you keep it straight. You can even color code if necessary while you get the hang of it.

 

Remember, the sum of all angles inside a triangle is 180º.

 

Given: ∠A = ∠D = 46º

 

Since you were vague in your description, I do not know which angle m∠39º is referring to, I will show you the possible answers.

 

If you meant ∠B = ∠E = 39º, then

∠C = ∠F = 180º - 39º - 46º

∠C = ∠F = 95º

 

If you mean ∠C = ∠F = 39º then guess what, that's your answer!

 

Remember, since similar triangles have identical angles, if they give you just one angle, (e.g. ∠B = 39º) then you know its corresponding angle, ∠E = 39º.

Answer 2

Byron correctly points out that the question is a bit ambiguous.

 

If m<B=39, then m<F=95.

If m<C=39, then m<F=39!

 

You appeared to be in a hurry to get your answer, Stephanie, that you left out this critical detail!