How to write page 43 13 of the first volume of ninth grade mathematics published by People's Education Press?

A hexagon, each point can have three diagonal lines, where every two lines are repeated, and 6*3/2 = 9.

7-sided, each point can have 4 diagonals, in which every two are repeated, 7*4/2 = 14.

An octagon, each point can have five diagonals, in which every two are repeated, and 8*5/2 = 20.

N sides, each point can have n-3 diagonal lines, where every two lines are repeated, n*(n-3)/2.

It is an octagon.

The formula of diagonal number of polygon is n(n-3)/2. If the convex polygon * * * has 20 diagonals, then n(n-3)/2=20 and the solution is n=8.

So this polygon is octagonal.

Secondly, if it is 18, there should be:

n(n-3)/2= 18

n(n-3)=36

N 2-3n-36 = 0 Solving this equation shows that n is not an integer, so there is no polygon with diagonal 18.