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Yes, 2 angles can have 3 points in common. Two angles of the same number of degrees can be superimposed on each other and would share all points. Or, you could choose 3 points on one line segment, while having two other line segments which do not share points, and which delineate different angles.
i think is call adjacent.. not sure
Adjacent angles
they share 2 points
Perpendicular lines will only share one point: the point of intersection, where the two lines meet.