How many sides can two congruent angles share? explain.

Any two congruent angles will have the same corresponding sides because the term congruent itself means equal. Thus, the measure of the angles will be equal. Note that we are talking about correspondence, not about the fact that the angles must share the same sides because two congruent angles don't have to point in the same direction, they don't have to be on similar sized lines, the only sufficient condition is that they have the same angle. Therefore they can (or not) share two sides. See the figure below.