In a certain pentagon, the interior angles are and where are integers strictly less than&

Question

In a certain pentagon, the interior angles are and where are integers strictly less than&

0

1379

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+1310

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