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In a certain pentagon, the interior angles are a, b,c, d,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?

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What is the area of the triangle 10 13 12