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?

Pungce
Sep 21, 2018

#2**+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 :)

Melody
Sep 22, 2018