A polygon has each interior angle measuring 175°. Determine the number of side of the polygon.

The formula for the interior angle of a regular polygon with $n$ sides is given by:

$$\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}$$

We are given that the interior angle is $175^\circ$. Substitute this value into the formula:

$$175^\circ = \frac{(n-2) \times 180^\circ}{n}$$

$$175n = 180n - (2 \times 180)$$ $$175n = 180n - 360$$

Subtract $180n$ from both sides.

$$175n - 180n = -360$$ $$-5n = -360$$

$$n = \frac{-360}{-5}$$ $$n = 72$$

The number of sides of the polygon is 72.

The number of sides of the polygon is $\text{72}$.