Opposite Rays
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-- Two rays with a common endpoint form an angle. -- If they have a common endpoint, then they are collinear. So I guess, technically, the conditions described in the question aren't possible.
Line
Two rays with the same endpoint form an angle. A ray is a part of a line that starts at a particular point and extends infinitely in one direction. When two rays share the same endpoint, they create an angle that is measured by the amount of rotation from one ray to the other. The common endpoint is called the vertex of the angle.
They are rays that lie on the same line. For example draw a horizontal line. Now put 3 points anywhere on that line. Next draw 3 rays, some going to the left, some going to the right. These rays are collinear.
A vertex.