An angle.
Angle
Yes.
Yes.
what is a ray
An angle.
vertex
Angle
Yes.
Two rays that share an endpoint form an angle.
An angle is the union of two rays with a common endpoint.
An angle is formed by two rays with a common endpoint.
a vertex
Yes.
what is a ray
-- 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.
an angle precisely defined as the common endpoint of two rays