A polygon is a plane shape with straight sides

Suppose,

The number of sides=n

so, every interior angles= $(180\times \dfrac{n-2}{n})^\circ$

So,according to the condition now we get,

$180\times \dfrac{n-2}{n}=156$

$or,180(n-2)=156n$

$or,(180-156)n=360$

$or,24n=360$

$or,n=\dfrac{360}{24}$

$\large\boxed{or,n=15}$

Each exterior angle= $180-156=24$ .we know sum of all exterior angles is 360°.therefore answer is $\frac{360}{24}=15$

$\frac{360}{(180 - n)}$ .

$\frac{360}{(180 - 156 = 24)}$ .

$\frac{360}{24} = 15$

$\therefore$ the answer is $\boxed{15}$

The sum of the interior angles of a regular polygon is given by $s=(n-2)(180)$ where $n$ is the number of sides. So the measure of one interior angle is $\dfrac{s}{n}$ . Then

$\dfrac{s}{n}=156$ or $s=156n$

Substituting the above in the formula, we have

$156n=(n-2)(180)$

$156n=180n-360$

$24n=360$

$n=\boxed{15}$