The formula for the interior angle of a regular polygon with n sides is given by \((n-2) \times \frac{180}{n}\). Since the size of each interior angle is 160°, we can set up the equation: \((n-2) \times \frac{180}{n} = 160\). Solving this equation for n, we get:

\[(n-2) \times \frac{180}{n} = 160\]

\[180n - 360 = 160n\]

\[20n = 360\]

\[n = 18\]

So the regular polygon has 18 sides.