`r`-sided polygons are formed by joining the vertices of an `n`-sided polygon. Find the number of polygons that can be formed, none of whose sides coincide with those of the `n`-sided polygon.

Find the number of diagonals in the convex polygon of n sides .

Find the number of diagonals in the convex polygon of n sides .

Find the number of diagonals in the convex polygon of n sides .

A regular polygon of 10 sides is constructed. Triangles are formed joining vertices of the polygon. Find the number of triangles (i) if two sides of trinangle coincide with the sides of polygon. (ii) if only one side of triangle coincide with the side of polygon.

A regular polygon of 10 sides is constructed. Triangles are formed joining vertices of the polygon. Find the number of triangles (i) if two sides of trinangle coincide with the sides of polygon. (ii) if only one side of triangle coincide with the side of polygon.