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Angle is a space between two lines or surfaces that meet at one point, which you measure in degrees.
it if called a edge for a 3D shape
Not in Euclidean Geometry. Euclid's 5th axiom is that parallel lines never meet. However, unlike the first 4 axiom, it is impossible to prove the 5th axiom; depending upon the situation, you can either assume that parallel lines meet or don't; when they do meet, there are some very interesting consequences (for example, the possibility of a hyperbolic space). To my knowledge, if they meet, they are intersecting/perpendicular lines.
An angle is formed where two lines meet. Parallel lines do not meet. Therefore they do not form an angle. So there is no angle to have a name. So no name.
Parallel lines are two 1-dimensional objects that do not meet. Parallel planes are two 2-dimensional objects that do not meet.