Question

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?

Answer 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 )

Answer 2

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

Answer 3

and the median is not 61 as well

Answer 4

61 is middle angle since its the median

Answer 5

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

Answer 6

so we have

-- -- 61 -- --

Answer 7

yes, you are right

Answer 8

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

Answer 9

yes, you are right

Answer 10

what if we had 61 , 61,61
how many degrees left?

540 - 183 = 357
so other 2 angles could be 179 and 178

Answer 11

that would fit

Answer 12

61,61,61,178,179

Answer 13

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

Answer 14

@mathmate @amistre64

Answer 15

@Michele_Laino

Answer 16

- hasn't that list only got one mode?

Answer 17

its an odd question

Answer 18

- 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

Answer 19

@Kainui

Answer 20

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

Answer 21

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.!!!

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

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