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In a certain pentagon, the interior angles are a, b, c, d, and e degrees 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 degrees and there is only one mode, then what are the degree measures of all five angles?

 

I've tried 61, 61, 61, 178, 179, but I have no idea what to do next.

Thank you!!!

 May 20, 2023
edited by Guest  May 20, 2023
 #1
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Well, you have solved the question, so what else is there to do? The median is 61 and the mode is 61 and the sum of the 5 angles (61 + 61 + 61 + 178 + 179)=540 degrees - which is the sum of interior angles of a pentagon. And of course, the 5 angles are all < 180 degrees.

 May 20, 2023
 #2
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I have to prove why other possibilities don't work. I'm working on it right now.

Thanks!

Guest May 20, 2023

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