Question

a polygon has 27 diagonals. how many sides does it have?

with explaination
because I have exam tomorrow ​

Answer 1

Answer:

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Answer 2

${ \green{ \bf{ANSWER:}}}$

$Number \: of \: diagonals = \frac{n(n - 3}{2} \\ \\ = > 27 = \frac{n(n - 3)}{2} \\ \\ = > 54 = n(n - 3) \\ \\ = > 54 = {n}^{2} - 3n \\ \\ = > {n}^{2} - 3n - 54 = 0 \\ \\ = > {n}^{2} - 9n + 6n - 54 = 0 \\ \\ = > n(n - 9) + 6(n - 9) \\ \\ = > (n - 9)(n + 6) = 0 \\ \\ = > so \: \: \: n \: = 9 \: or \: - 6$

But, number of sides can't be negative.

So, number of sides = 9