# 6. Variant 1.

A diagonal of a 20-gon divides it into a 14-gon and an 8-gon (see figure). How many of the remaining diagonals of the 20-gon intersect the highlighted diagonal? The vertex of the 14-gon is not considered an intersection.

![](https://cdn.mathpix.com/cropped/2024_05_06_9d8fa1da0443074cdbacg-5.jpg?height=605&width=599&top_left_y=1855&top_left_x=709)
Answer: 72.

Solution. On one side of the drawn diagonal, there are 12 vertices, and on the other side - 6. Therefore, $12 \cdot 6=72$ diagonals intersect the highlighted one.