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The sum of all the interior angles of a regular polygon is $1260^{\circ}$, then find the numbers of sides.
Given: The sum of all the interior angles of a regular polygon is $1260^{\circ}$.
To do: To find the number of sides in the given polygon.
Solution:
As known that, Sum of measures of all interior angles of polygons $=( 2n−4)\times90^o$
Given, interior angle$=1260^o$
$\Rightarrow 1260=( 2n−4)×90^o$
$\Rightarrow 2n-4=\frac{1260}{90}$
$\Rightarrow 2n−4=14$
$\Rightarrow 2n=14+4$
$\Rightarrow 2n=18$
$\Rightarrow n=\frac{18}{2}$
$\Rightarrow n=9$
Therefore, the number of sides in a polygon is $9$.
Updated on: 10-Oct-2022
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