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In a certain pentagon, the interior angles are\(\)    \($a^\circ,$ $b^\circ,$ $c^\circ,$ $d^\circ,$ and $e^\circ,$\)      where  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\( $61^\circ$\)  and there is only one mode, then what are the degree measures of all five angles?

 Sep 21, 2018
 #1
avatar+4084 
+3

I think it is: 61, 61, 61, 178, 179, and no angle can be < 61 degrees.

 Sep 22, 2018
 #2
avatar+100063 
+2

 

In a certain pentagon, the interior angles are   a,b,c,d,e       where  are integers strictly less than 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?

 

Angle sum of a pentagon is  180*3 = 540 degrees. 

 

540-61= 479

479/4=119.75      since 2 are very little,  2 must be really big.

179+179=358

60+60=120

358+120=478  which is one too little

 

60,60,61,179,179 = 539    1 to little and there is 2 modes

60,61,61,179,179 = 540     right size but 2 modes

61,61,61,178,179 = 540     right size and only one mode.    

 

Same as Tertre so that is great :)

 Sep 22, 2018

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