A regular polygon has interior angle $ 160^\circ $.How many sides does it have?

We are given a regular polygon with an interior angle $160^\circ$ and need to find the number of sides $n$.

The formula for the interior angle of a regular polygon is:

$ \text{Interior angle} = \frac{(n-2) \cdot 180}{n} $

Set it equal to $160$:

$ \frac{(n-2) \cdot 180}{n} = 160 $

Multiply both sides by $n$:

$ (n-2) \cdot 180 = 160 n $

 180n - 360 = 160n

20n = 360

n = 18