The interior angle of a regular polygon can be calculated using the formula:

\[ \text{Interior Angle} = \frac{(n-2) \times 180°}{n} \]

Where \( n \) is the number of sides of the polygon.

Given that the interior angle is \( 140° \), we can set up the equation:

\[ 140° = \frac{(n-2) \times 180°}{n} \]

To solve for \( n \), first multiply both sides by \( n \):

\[ 140°n = (n-2) \times 180° \]

Expand the right side:

\[ 140°n = 180°n - 360° \]

Now, isolate \( n \) on one side:

\[ 360° = 180°n - 140°n \]

\[ 360° = 40°n \]

Divide both sides by \( 40° \):

\[ n = \frac{360°}{40°} = 9 \]

So, the polygon has 9 sides.