Knowee
Questions
Features
Study Tools

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

Question

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

Group of answer choices

  • 5 sides
  • 6 sides
  • 8 sides
🧐 Not the exact question you are looking for?Go ask a question

Solution

1. ### Break Down the Problem

To find the number of sides in a regular polygon where each internal angle measures 120120^\circ, we need to use the formula for the internal angle of a regular polygon, which is:

Internal Angle=(n2)×180n \text{Internal Angle} = \frac{(n-2) \times 180}{n}

where nn is the number of sides.

2. ### Relevant Concepts

We know:

  • Given internal angle = 120120^\circ.
  • Set the equation for internal angle equal to 120120^\circ and solve for nn.

3. ### Analysis and Detail

Setting up the equation:

120=(n2)×180n 120 = \frac{(n-2) \times 180}{n}

Multiplying both sides by nn:

120n=(n2)×180 120n = (n-2) \times 180

Expanding the right side:

120n=180n360 120n = 180n - 360

Rearranging to isolate nn:

360=180n120n 360 = 180n - 120n 360=60n 360 = 60n n=36060=6 n = \frac{360}{60} = 6

4. ### Verify and Summarize

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

Internal Angle=(62)×1806=4×1806=7206=120 \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.

This problem has been solved

Similar Questions

How many sides does a polygon have if each of its interior angles measures 156°?

The measure of an interior angle of a regular polygon is 156°. Find the number of sides in the polygon.

Each exterior angle of a regular polygon measures 9°. How many sides does the polygon have?Choices:- 36 45 40 30

If an exterior angle of a regular polygon measures 45°, how many sides does the polygon have?

How many sides does a regular polygon have if each of the exterior angles measures 30 degrees?There are number of sides

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.