Congruent Angles
Congruent Angles have the same angle (in degrees or radians). That is all.
These angles are congruent.
They don't have to point in the same direction.
They don't have to be on the same line.
Just the same angle.
Example: Kite
The angles formed by the left and right corners of this kite are congruent.
But not the top and bottom.
Example: Two angles are congruent, one measures 35°, what does the other measure?
The other angle measures 35° also.
Congruent - why such a funny word that basically means "equal"? Maybe because they are only "equal" when laid on top of each other. Anyway it comes from Latin congruere, "to agree". So the angles "agree".