Show that a convex polygon of m sides has `(m(m-3))/2` diagonals

In a convex polygon of 6 sides two diagonals are selected at random. The probability that they interesect at an interior point of the polygon is

Consider the convex polygon, which has 35 diagonals. Then match the following column. Column I, Column II Number of triangles joining the vertices of the polygon, p. 210 Number of points intersections of diagonal which lies inside the polygon, q. 120 Number of triangles in which exactly one side is common with that of polygon, r. 10 Number of triangles in which exactly two sides are common with that of polygon, s. 60

(i) Find the number of sides of a polygon if it has 35 diagonals. (ii) How many triangles can be formed with the vertices of an octagon?

STATEMENT-1 : If the angle of a convex polygon are in A.P. 120^(@) , 125^(@) , 130^(@) …, then it has 16 sides and STATEMENT-2 : The sum of the angles of a polygon of x sides is (n -2) 180^(@)

The number of diagonals of a polygon of 15 sides is:

Number of quadrilaterals which can be constructed by joining the vertices of a convex polygon of 20 sides if none of the side of the polygon is also the side of the quadrilateral is

Number of quadrilaterals which can be constructed by joining the vertices of a convex polygon of 20 sides if none of the side of the polygon is also the side of the quadrilateral is

The number of pairs of diagonals of a regular polygon of 10 sides that are parallel are

The number of diagonals of a convex polygon is 15 less than 4 times the number of its sides. The number of sides of the polygon be

Find the number of triangles which can be formed having vertices at angular points of a convex polygon of m sides.