$A$ polygon has $35$ diagonals,then the number of its sides is

There are $20$ straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined,then the number of new line segments formed is

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is:

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?

$A$ polygon has $54$ diagonals. Then,the number of its sides is