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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 $60^\circ$, then what are the possible degree measures of all five angles?

 Dec 31, 2020
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The angles of the pentagon could be 58, 59, 60, 178, and 179.

 Dec 31, 2020

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