A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find the number of sides of a regular polygon if one interior angle is 120 degrees. A.) 6 B.) 5 C.) 4 D.) 3

  • This Question is Closed
  1. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know the formula that tells you the sum of the measures of the interior angles of a polygon?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No

  3. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is the formula: \(S = (n - 2)180\) where S = sum of the measures of the interior angles, and n = number of sides.

  4. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know what "regular" means when you say regular polygon?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    When all angles are equal?

  6. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It means a polygon that has all sides of the same length and all interior angles of the same measure.

  7. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct. All angles are congruent, and all sides are congruent.

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So would it be 3?

  9. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now we can solve this problem. Since you are dealing with a regular polygon, all angles have the same measure. Let's say the sum of the measures of the interior angles is S. Also, let's say your polygon has n sides. Then each angle would have the measure S/n Ok so far?

  10. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, it's not 3.

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just follow what I am explaining . We'll find the answer soon.

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay!

  13. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If the sum of the measures of the interior angles is S and the polygon has n sides, then each interior angle measures S/n.

  14. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We have a formula for the sum of the measures of the interior angles. \(S = (n - 2)180\) If we divide it by n, the number of sides, we will have the measure of one angle. \(\dfrac{S}{n} = \dfrac{(n - 2)180}{n} \) is the measure of one angle. We are told one angle measures 120 deg, so we set our expression equal to 120 and ewe solve for n. \(\dfrac{(n - 2)180}{n} = 120\)

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I think I got it now! thank you so much!

  16. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now we have to solve that equation for n. We multiply both sides by n: \((n - 2)180 = 120n\) Distribute 180 on the left side: \(180n - 360 = 120n\) Subtract 120n from both sides, and add 360 to both sides: \(60n = 360\) Divide both sides by 60: \(n = 6\) Since n is the number of sides of the polygon, we can answer: The polygon has 6 sides.

  17. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome.

  18. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.