There are 10 lines in a plane, each intersecting each other. No three lines pass through the same point.?

Question

There are 10 lines in a plane, each intersecting each other. No three lines pass through the same point. At how many points do the lines intersect and into how many regions do they seperate the plane?

Answer 1

Intersections are 45. Each line is intersected by 9 others so it has 9 intersection points on it. 10 lines * 9 points on each equals 90, but you have to divide by 2 because each intersection is bisected by two lines.

The other trickier. I think the answer is 2+2+3+4+5+6+7+8+9+10 or 56 but I could be wrong. My idea is that the first line splits the plane into 2 parts, the second, 2 more parts, the third adds 3 more, and the 4th line 4 more, etc.

Answer 2

A star