Respuesta :

23 gon polygon has 230 diagonals

Solution:

The number of diagonals in polygon is given as:

[tex]\text{Number of diagonal } =\frac{n(n-3)}{2}[/tex]

where n is the number of polygon sides

Given that,

Consider a regular 23-gon

n = 23

Substitute n = 23 in above formula

[tex]\text{Number of diagonal } =\frac{23(23-3)}{2}\\\\\text{Number of diagonal } =\frac{23 \times 20 }{2}\\\\\text{Number of diagonal } = 23 \times 10\\\\\text{Number of diagonal } = 230[/tex]

Thus, a 23 gon polygon has 230 diagonals

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