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In a certain pentagon, the interior angles are a,b,c,d and e 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 and there is only one mode, then what are the degree measures of all five angles?

Guest Sep 19, 2017

#1**+1 **

In a certain pentagon, the interior angles are a,b,c,d and e 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 and there is only

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The sum of all the interior angles of a pentagon = 540°

Note that if we require* integer* solutions....we will have a problem

If the median angle is 61° and we have only a * single* mode....

But note that the sum of the three smallest angles [ 59° + 60° + 61°] = 180°.....so....this means that the remainder of the angles must sum to 540 - 180 = 360°.....but this would mean that * one *of the largest two angles will have to be > 180° [because of the single mode requirement] and this isn't allowed

CPhill Sep 20, 2017