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

 May 2, 2018
 #1
avatar+98091 
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Here's one possibility  [ but maybe not the only one ]

The sum of the interior angles  = 540°

 

Let the smallest angle  = 60°

Let the next two angles   =  60.5°    and 61.5°

Note that the median  =  [ 60.5  + 61.5)  / 2  = 61°

 

Thw sum of the angles, so far, is  182° 

So...the sum of the other two angles will be     540  - 182  =  358°

Let the next two angles  = 179°   

 

The sum of the angles is 

 

[60 + 60.5 + 61.5 + 179 + 179]  =  540°

 

The median  =  61°    and   there is only one mode,  179°

 

cool cool cool

 May 2, 2018

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