Quiz

Why?

Well, I think it's because when you attach a parallelogram to any polygon, it either won't change the number of angles, or it will decrease them by two, or decrease them by four, or increase them by two, or increase them by four. This is easy to show in a diagram. A parallelogram has 4 angles, so when attaching other parallelograms to it, we will always get a figure with an even number of angles. I think there's something about topology here, but I don't know topology.