Find the number of sides of a regular polygon whose in each interior angle is of measure 120°

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°.

Learn how to determine the number of sides of a regular polygon when each interior angle measures 120°. This problem involves using the formula for the interior angle of a polygon and solving a linear equation. Suitable for Grades 7-9 students and anyone interested in geometry and polygon properties.

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