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Suppose the polygon has V vertices.Then sum of interior angles is (V - 2)*180 degrees = 1980 degrees => V - 2 = 1980/180 = 11 => V = 13 A polygon with V vertices has V*(V-3)/2 = 13*10/2 = 65 diagonals.
There are always 2 diagonals in any quadrilateral whether or not it is irregular or regular
An n sided polygon has n*(n-3)/2 diagonals.
It can be :- 1- a parallelogram 2- Square if diagonals are perpendicular and congruent 3- Rectangle if diagonals are congruent 4- Rhombus if diagonals are perpendicular
A polygon with n sides has n*(n-3)/2 diagonals. Simple as that. So a 9 sided polygon has 9*6/2 = 27 diagonals.