Number of sides

Assuming the polygon is regular, each interior angles is of size $\frac{1260}{n}$ . This makes each exterior angle $180-\frac{1260}{n}$ . Now the exterior angles of any polygon add up to $360$ degrees so each exterior angle would be $\frac{360}{n}$ . Therefore:

$180-\frac{1260}{n}=\frac{360}{n}$

$180n-1260=360$

$180n=1620$

$n=\boxed{9}$

In a polygon, the sum of interior angles is

$s=(n-2)(180)$

Substituting, we get

$1260=(n-2)(180)$

Dividing both sides by $180$ , we get

$7=n-2$

Adding $2$ to both sides, we get

$9=n$