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?

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

Step-by-step 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

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation:

150

step-by-step explanation:

(sorry i'm not typing it again just read the other two explanation sections i just typed it'll be the same.)