$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is

$A$ regular polygon has $170$ diagonals. Then the measure of the interior angle of the polygon is

Some couples participated in a mixed doubles badminton tournament. If the number of matches played,such that no couple played in a match,is $840$,then the total number of persons who participated in the tournament is $........$.

$T_m$ denotes the number of triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$,then $m$ is equal to

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is: