Final answer:
Two angles are congruent if they are equal in measure, not necessarily when they sum to 90 or 180 degrees or are perpendicular, as those terms describe complementary, supplementary, and perpendicular angles respectively.
Step-by-step explanation:
Two angles are congruent if they are equal in measure. This means that the degree measure of one angle is exactly the same as the degree measure of the other angle, irrespective of their orientation or position. Congruent angles might be found in various geometric shapes, such as triangles, where we know that the sum of the three angles adds up to 180 degrees, or they might be corresponding angles formed by a pair of parallel lines cut by a transversal.
The other options given, such as angles summing to 90 degrees, summing to 180 degrees, or being perpendicular, describe other specific angle relationships. For instance, angles that sum to 90 degrees are complementary angles, and those that sum to 180 degrees are supplementary angles. Perpendicular lines intersect to form a 90-degree angle, and such angles are not necessarily congruent unless they are also equal to 90 degrees each.