The measurement of each internal angle of a regular polygon is 120°. How many sides does it have?Group of answer choices5 sides6 sides8 sides

1. ### Break Down the Problem

To find the number of sides in a regular polygon where each internal angle measures $120^\circ$, we need to use the formula for the internal angle of a regular polygon, which is:

$\text{Internal Angle} = \frac{(n-2) \times 180}{n}$

where $n$ is the number of sides.

2. ### Relevant Concepts

We know:

• Given internal angle = $120^\circ$.
• Set the equation for internal angle equal to $120^\circ$ and solve for $n$.

3. ### Analysis and Detail

Setting up the equation:

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

Multiplying both sides by $n$:

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

Expanding the right side:

$120n = 180n - 360$

Rearranging to isolate $n$:

$360 = 180n - 120n$ $360 = 60n$ $n = \frac{360}{60} = 6$

4. ### Verify and Summarize

To verify, we can substitute $n = 6$ back into the internal angle formula:

$\text{Internal Angle} = \frac{(6-2) \times 180}{6} = \frac{4 \times 180}{6} = \frac{720}{6} = 120^\circ$

This verifies our solution is correct.

Final Answer

The regular polygon has 6 sides.