If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
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There are 20 common points.
20....or maybe 18
Here are some: They can be (1) coincident, (2) intersecting at one point, (3) coplanar but non-intersecting (ie parallel), (4) non-coplanar, non-parallel and non-intersecting (eg paths of a rail line and of an elevated road going over it - from above, they may appear to intersect but they do not), (5) intersecting at two points (eg longitudes on the earth). etc.
when a pair of angles/numbers have 1 of the same numbers (for example: 4,3,5,6 and 1,2,3,5,4 have intersecting numbers (4,3, and 5) and also points (4,5) and (4,6) Haver them too (because 4 stands for the 'x' the if you were to plot that on a graph, the points would intersct one another)
The greatest number of intersection points with just four lines is 6.