From this we can also know that the number of vertex angles = the number of intersection points * 2; Number of adjacent complementary angles = number of intersection points * 4
Considering that there are many straight lines,
Draw a third straight line, as long as it is not parallel to the first two, it will intersect with the first two straight lines, and add two intersections, *** 1+2 intersections.
Draw the fourth straight line, as long as it is not parallel to the first three, it will intersect with the first three straight lines, and add three intersections, *** 1+2+3 intersections.
Draw the fifth straight line, as long as it is not parallel to the first four straight lines, it will intersect with the first four straight lines, and add four intersections, *** 1+2+3+4 intersections.
Draw the nth straight line, as long as it is not parallel to the previous n- 1, it will intersect all the n- 1 straight lines, plus n- 1 intersection points, * *1+2+3+4+...+n-/kloc-0.
Therefore, the number of intersection points of n lines that are not parallel to each other =1+2+...+(n-1) = n (n-1)/2.
So: the number of vertex angles is n(n- 1) pairs; The number of complementary angles is 2n(n- 1) pairs.
Of course, three or more straight lines are not considered to intersect at the same point.
Now let's consider this situation: when (x- 1) straight lines intersect at the same point, assuming that the number of antipodal angles is n now, when a new straight line passes through the intersection of common * * *, it will form a new antipodal angle with all existing straight lines, and the logarithm of this new antipodal angle is 2(x- 1.
Therefore, even if all straight lines intersect at one point: the number of vertex angles is n(n- 1) pairs; The number of adjacent complementary angles is 2n(n- 1) pairs.