To find the number of sides of a regular polygon given that each interior angle measures 120°, we can use the formula for the interior angle of a regular polygon:

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

Where:

• $n$ is the number of sides of the polygon.

Given that the interior angle is $120^\circ$, we can set up the equation:

$\frac{(n-2) \times 180^\circ}{n} = 120^\circ$

Now, solve for $n$:

1. Multiply both sides by $n$ to eliminate the fraction:

$(n-2) \times 180^\circ = 120^\circ \times n$

2. Expand and simplify:

$180n - 360 = 120n$

3. Subtract $120n$ from both sides:

$60n = 360$

4. Divide by 60:

$n = \frac{360}{60} = 6$

So, the polygon has 6 sides.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you calculate the exterior angle of a regular polygon?
2. What is the relationship between the interior and exterior angles of a regular polygon?
3. How does the number of sides affect the measure of each interior angle in a regular polygon?
4. Can a regular polygon have an interior angle of 90°? If yes, how many sides does it have?
5. What are the properties of a regular hexagon?

Tip: Remember that the sum of the interior and exterior angles at any vertex of a polygon is always 180°.