Because line AB is parallel to CB, we know that angles EGB and EHD are corresponding angles.
Corresponding angles are congruent. Why, you ask? Well if you take a look at the diagram, you'll realize that angles EGB and AGH are vertical angles. Because of this, they're congruent. AGH and EHD are alternate interior angles, which are congruent.
Knowing that EHD is a corresponding angle to EGB, we know that the measure is 57 degrees.
