A regular polygon with an interior angle of 135° has 8 sides.

The formula for the interior angle of a regular polygon is

\(\frac{(n-2) \times 180^\circ}{n}\), where n is the number of sides.

If we let the interior angle be 135°, we can solve for n: \(\frac{(n-2) \times 180^\circ}{n} = 135^\circ\).

This simplifies to \(180n - 360 = 135n\), which further

simplifies to:

\(45n = 360\).

Dividing both sides by 45, we get \(n = 8\). Therefore, a regular polygon with an interior angle of 135° has 8 sides.