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- anonymous

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?

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- anonymous

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- welshfella

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 )

- welshfella

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

- Loser66

and the median is not 61 as well

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- welshfella

61 is middle angle since its the median

- Loser66

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

- welshfella

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

- Loser66

yes, you are right

- welshfella

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

- Loser66

yes, you are right

- welshfella

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

- welshfella

that would fit

- welshfella

61,61,61,178,179

- Loser66

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

- Loser66

- Loser66

- welshfella

- hasn't that list only got one mode?

- welshfella

its an odd question

- welshfella

- 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

- Loser66

- anonymous

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

- Loser66

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.!!!

- anonymous

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

- Loser66

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.

- anonymous

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

- welshfella

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

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