8,9 |
| :---: | :---: | :---: |
|  | [ Systems of points and segments (other).] |  |
|  | [ Multiplication rule ] |  |
|  | [ Arbitrary polygons ] |  |

How many diagonals does a convex:
a) 10-gon;
b) $k$-gon $(k>3)$ have?
b) Each pair of points forms a segment: a side or a diagonal.

By subtracting the number $k$ of sides from the number $C_{k}^{2}$ of pairs, we get the number of diagonals.

## Answer

a) 35 ; b) $\frac{k(k-3)}{2}$ diagonals.