SOLUTION: Can you help me answer this? Thank you very much :) There is a seven-sided polygon. If there are no three diagonals of this polygon intersected in a common point, then the points

Question 1006379: Can you help me answer this? Thank you very much :)
There is a seven-sided polygon. If there are no three diagonals of this polygon intersected
in a common point, then the points of intersection of these diagonals will divide the diagonals
into how line segments?
a. 80
b. 84
c. 88
d. 90
e. 108
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

Coming from each vertex, there are diagonals, skipping over one vertex, and skipping over two vertices.
Multiplying diagonals per vertex times vertices, we would count each diagonal twice, so there is a total of diagonals.
Of those diagonals, skip one vertex and skip two vertices.
The diagonals that skip over one vertex are intersected by the diagonals coming from the skipped vertex,
so they are divided into line segments.
The diagonals that skip over two vertices are intersected by diagonals, coming from each skipped vertex,
so they are divided into line segments.
The total number of line segments in the diagonals is
.
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