A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

In a certain pentagon, the interior angles are a,b,c,d,e degrees where a,b,c,d,e are integers strictly less than 180. ("Strictly less than 180" means they are "less than and not equal to" 180.) If the median of the interior angles is 61 degrees and there is only one mode, then what are the degree measures of all five angles?

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

    i imagine there is no one answer to this question The following list of angles would meet the requirements 59,60,61,61,149,150 ( = 540 degrees )

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

    ooops thats wrong - I have 6 angles there 1 only 5 in a pentagon!

  3. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and the median is not 61 as well

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

    61 is middle angle since its the median

  5. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i don't get what "there is only one mod" mean

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

    so we have -- -- 61 -- --

  7. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, you are right

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

    - i guess one angle occurs twice? or it could occur 3 times?? - thats still only one mod right?

  9. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, you are right

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

    what if we had 61 , 61,61 how many degrees left? 540 - 183 = 357 so other 2 angles could be 179 and 178

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

    that would fit

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

    61,61,61,178,179

  13. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am pretty sure that the sentence "there is only one mod" has some meaning and it limits the answer. @satellite73

  14. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathmate @amistre64

  15. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Michele_Laino

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

    - hasn't that list only got one mode?

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

    its an odd question

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

    - i think this might be the only solution because 3 61's is the only combination that will all ow the last 2 numbers to less than 180 degrees and different

  19. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Kainui

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

    Please 61 is the Median and yes two angles can be 61 which means the other 3 have to be same to be a mode of which there can be only one. Now 61*2=122 So, 540-122= 418 418/3 = 139.33333.. Now something isn't right here or my understanding incorrect

  21. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We can turn it into one mode. :) as what welshfella said, it can be 61-61- 61 and n, n 540-3*61 = 357, that means n = 178.5 to turn it to multiple of 61, we do 61 * factor = 178.5 , hence factor = 178.5/ 61=(357/122) hence the angles are 61,61,61, (357/122)61, (357/122)61 hahaha... I am crazy.!!!

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

    Loser.. as the name suggest... I am serious here.. need to solve this real quick

  23. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, I am a big Loser. I want to study also. That was why I tagged many others to get help for YOU. If my solution doesn't satisfy you, I am so sorry.

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

    u r not a loser.. I cant understand why we convert median to mode.. there is a catch here... also I tired to solve.. what is wrong in that can you suggest. Name or no name.. whats in it ? A guide can be a mis-guide.. sorry I didn't meant to be rude

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

    what is wrong with my solution? It fits all the requirements

  26. 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.