Tried Everything I could. I'm stuck.

Question

If a translation maps ∠D onto ∠B, which of the following statements is true?

 ∠E ≅ ∠C

  ≅ 

 ∠E ≅ ∠A

  ≅ 

I believe it is the third option but I am not sure.

Answer 1

The problems is correctly formulated. I would only add specific names for the angles. ∠D means ∠EDC, ∠E means ∠CED. The fact that a translation maps ∠D onto ∠B means that these two angles are congruent as translation is simply a rigid movement. Since ∠D and ∠B are congruent, lines AB and ED must be parallel as ∠D and ∠B are corresponding angles. Thus, ∠E ≅ ∠A as these are now also corresponding angles.