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How Many Angles Are Formed When Two Lines Intersect?

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Oddman answered
The intersection of 2 lines forms 4 rays. It only takes 2 rays to determine an angle. Any one of the 4 rays can be taken to be the clockwise side of the angle, and any one of the remaining 3 rays can be taken to be the counterclockwise end of the angle, for a total of 12 angles.

Suppose the point of intersection is A, and the rays are identified AB, AC, AD, AE. The following 12 angles are formed:
BAC, BAD, BAE, CAD, CAE, DAE, EAD, EAC, DAC, EAB, DAB, CAB.

Of course, angles BAC and CAB add to 360°, as do other "forward/reverse" pairs. If the two lines are BD and CE, then several of the angles are identically equal to 180°: BAD, DAB, CAE, EAC.

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