Question

Number of polygons in a diagonal is 27 how many sides does it have

Answer 1

The question should be ' Number of diagonals in a polygon is 27 '

Anyways,  we have the formula for number of diagonals in a polygon

number of diagonals, $d = \frac{n(n-3)}{2}$, where $n$ is the number of sides in the polygon

$27 = \frac{n(n-3)}{2}$

$54 = n^2-3n$

$n^2-3n-54=0$

$n^2+6n-9n-54=0$

$n(n+6)-9(n+6)=0$

$(n-9)(n+6)=0$

$n=9$  OR  $n= (-6)$

But since a polygon cannot have negative number of sides, $n=(-6)$ is rejected

Hence the polygon has 9 sides

That is, the polygon is a nonagon

HOPE IT HELPS !!