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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 $9$.

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