How many diagonals does the regular polygon have

Answers

Not 100% but I'm pretty sure 48.

23 gon polygon has 230 diagonals

Solution:

The number of diagonals in polygon is given as:

\text{Number of diagonal } =\frac{n(n-3)}{2}

where n is the number of polygon sides

Given that,

Consider a regular 23-gon

n = 23

Substitute n = 23 in above formula

\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

Thus, a 23 gon polygon has 230 diagonals

 90

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Work Shown:

n = number of vertices = 15

d = number of diagonals

d = \frac{n*(n-3)}{2}\\\\d = \frac{15*(15-3)}{2}\\\\d = \frac{15*12}{2}\\\\d = \frac{180}{2}\\\\d = 90\\

So there are 90 diagonals for this 15-gon.

The numerator n(n-3) is from the fact that there are n vertices, and for each vertex, there are n-3 points to connect to that will form a diagonal. Why n-3? The 3 comes from the fact that you cannot select the current point, or either neighboring point (on either side). So we ignore 3 points when forming diagonals for any vertex. That's why n drops to n-3.

The 2 in the denominator is to correct for double-counting. A diagonal like AB is the same as BA. The order does not matter when it comes to naming a segment.

3

Step-by-step explanation:

3

Step-by-step explanation:



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