I assume you mean that the line goes through a certain point. There is no limit to how many lines you can have through the same point.
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They are the arms of an angle.
Yes when two lines share a common end point an angle is formed
The only lines that are in the same plane that do not intersect are: 1. Lines of finite length (eg 1 6" line on the floor at one end of the room and another 8" line at the other end) 2. Parallel lines
a rainbow 
an angle