1 As a diagonal line passes through the same vertex of N polygon, N polygon can be divided into (n-2) triangles 10-2=8.

2 From the diagonal of n polygon =N(N-3)/2: N=7.

3,8+2 8+2= 10/0, 10 polygon.

4,5 diagonal lines of N- polygon =N(N-3)/2

5 and 9 diagonals of N- polygon =N(N-3)/2.

7. A vertex can draw n-3 diagonal lines and be divided into n-2 triangles.

8. Because the outer angle of a regular polygon is 40.

So each interior angle is 140.

According to the internal angle sum formula,

180(n-2)= 140n

The solution is n=9.

Let the number of sides of this polygon be n.

Because the sum of the inner angles of a polygon is equal to (n-2)× 180.

And because the sum of the outer angles of a polygon is equal to 360 degrees (360 degrees for any polygon).

So according to the meaning of the question: (n-2)× 180=360×2.

The solution of n-2=4

So n=6.

10.360

1 1.9

12.8 polygon

13. 135

14. Pentagon and decagon

Let one side be x and the other side be 2x.

4( 180-360/x)= 3( 180-360/2x)

x=5