What is the number of diagonals that intersect at a given vertex of a hexagon, heptagon, 30-gon and n-gon?

i. 9

ii. 14

iii. 405

iv.

Step-by-step explanation:

The number of diagonals in a polygon of n sides can be determined by:

where n is the number of its sides.

i. For a hexagon which has 6 sides,

number of diagonals =

                                   =

                                   = 9

The number of diagonals in a hexagon is 9.

ii. For a heptagon which has 7 sides,

number of diagonals =

                                   =

                                   = 14

The number of diagonals in a heptagon is 14.

iii. For a 30-gon;

number of diagonals =

                                          =

                                         = 405

The number of diagonals in a 30-gon is 405.

iv. For a n-gon,

number of diagonals =

The number of diagonals in a n-gon is

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step-by-step explanation:

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step-by-step explanation:

this is a parabola.