Single Choice

The expression for the number of diagonals that we make from one vertex of a $$n$$ sided polygon is:

A$$2n+1$$
B$$n-2$$
C$$5n+2$$
D$$n-3$$
Correct Answer

Solution

∙ For n=3, the polygon is a triangle in which there is no diagonal. The difference of number of sides and diagonals is (3−0=3)
∙ For n=4, the polygon is a quadrilateral in which number of diagonals from a vertex is 1. The difference of number of sides and diagonals is (4−1=3)
∙ For n=5, the polygon is a pentagon in which number of diagonals from a vertex is 2. The difference of number of sides and diagonals is (5−2=3)
∙ So, for a polygon of n sides, the number of diagonals from a vertex will be n−3
Hence, the correct option is (d)

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