Corresponding, 180 and Vertical Angles

When I drew this diagram I deliberately put in different sizes of lines to show the angles a b c and d. The lines for b and c are almost touching and I wanted to avoid this (I'll try harder in the future). They are different sizes so that they don't join together and also to tell you that it really doesn't matter what size these lines are. It is only important to be clear on what you are talking about.

Last time I looked at corresponding angles. In the diagram a and c are corresponding angles. Now look at c and d. If you know that 180 degrees is a straight line then you now know that c and d add up to 180 degrees. Just by simple manipulation of an equation you know that c + d = 180.
You know that c = 180 - d.
You know that d = 180 - c.

Also notice the angles a and b. Can you see that they are equal? Pick up two pens and make a similar shape and then change it to make a right-angle. The a and b angles remain equal however you move the pens. a and b are called vertical angles not because they are upright but because they share one point, the vertex where the pens cross.

That sums it up.