How do you know that the corresponding angle to the right angle is also 90º?

Its because its perpendicular and also because if the angle which is 90 degrees and if it is corresponding to another angle that angle would also be 90 degrees and so if there's and angle missing just look for the corresponding one and that one will be the same degree.

You know if it is a right angle or not because it has straight lines. It has to have to straight lines, making a little box. 
Well, the answer you could put is that the corresponding angle has the same characteristics as it, and you can form a little box at the beginning. ALSO, if you measured with a protractor, you would get exactly 90 degrees.