In a certain pentagon, the interior angles are a degrees, b degrees, c degrees, d degrees, and e degrees, where a,b,c,d 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?

plz tell me how you got the answer so i can understand.

SmartMathMan
Dec 20, 2017

#1**+2 **

I think the five degree measures are....

61, 61, 61, 178, 179

We know that the median is 61° .

And we know that the sum of the angles must be 540° .

In the list of angles from least to greatest, if we made the two to the left of the median any smaller, then we would have to make the two to the right of the median larger so that they will sum to 540.

Well if we made the first angle be 60°, then the 178° would have to become 179° and we would have two modes. And if we made the first two angles any smaller than that, then it would put the last two angles over 180°.

I hope that made some sense!

hectictar
Dec 21, 2017

#1**+2 **

Best Answer

I think the five degree measures are....

61, 61, 61, 178, 179

We know that the median is 61° .

And we know that the sum of the angles must be 540° .

In the list of angles from least to greatest, if we made the two to the left of the median any smaller, then we would have to make the two to the right of the median larger so that they will sum to 540.

Well if we made the first angle be 60°, then the 178° would have to become 179° and we would have two modes. And if we made the first two angles any smaller than that, then it would put the last two angles over 180°.

I hope that made some sense!

hectictar
Dec 21, 2017