Question

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?

Answer 1

61,61,61,178,179

Explanation:

your welcome. :)

Answer 2

least to greatest: {61, 61, 61, 178, 179}

Explanation:

If the third-largest angle is 61°, the smallest three angles cannot be larger than 183°. Since the total of all angles must be 540°, and the total of the largest two cannot be greater than 179°×2 = 358°, the sum of the smallest three must be at least 540° -358° = 182°.

So, the possible sets of angles with the smallest 3 totaling 182° or 183° are (in degrees) ...

{60, 61, 61, 179, 179} . . . . two modes

(61, 61, 61, 178, 179} . . . . . one mode -- the set you're looking for