All right angles are congruent.
All straight angles are congruent.
All zero angles are congruent.
All the angles of a regular polygon are congruent.
Vertical angles (the angles opposite one another when two lines intersect) are congruent.
When a transversal crosses parallel lines:
Corresponding angles are congruent.
Alternative Interior angles are congruent.
Alternative Exterior angles are congruent.
Finally, any angles with the same measure are congruent.
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Vertical angles must necessarily be congruent, however congruent angles do not necessarily have to be vertical angles. An example of congruent angles which are not vertical angles are the 3 interior angles of an equilateral triangle. These angles do not share the same vertex yet they are congruent.
they have 4 congruent angles
Vertical angles are always, by definition, congruent. Note: If the two vertical angles are right angles then they are both congruent and supplementary.
Two angles that are congruent have the same angle measurement.
A triangle with three congruent angles