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How many diagonals are there in a 50-sided polygon?

Answer 1

#1175#

The number of diagonals of an n-sided polygon is:

#(n(n - 3)) / 2#

It is very immediate to understand: from any vertex, you can draw diagonals to every other vertex, except three: the vertex itself, and the one immediately before and after.

So, for each of the #n# vertices you have #n-3# choices, for a total of #n(n-3)#

Nevertheless, you're counting each diagonal twice in this process, so you divide by two to get to the final formula.

So, you have

#\frac{50(50-3)}{2} = \frac{cancel(50)\cdot 47}{cancel(2)} = 25*47 = 1175#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.