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The number of degrees in the measures of the interior angles of a convex pentagon are five consecutive integers. What is the number of degrees in the largest angle?

 Apr 1, 2020
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 Apr 1, 2020
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Totally unrelated, but answering questions here is fun and I should do it more.

Impasta  Apr 1, 2020
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The number of degrees in the measures of the interior angles of a convex pentagon are five consecutive integers. What is the number of degrees in the largest angle?   

 

The sum of the interior angles of a polygon of n sides is (n – 2)(180) 

Thus the sum of the interior angles of a pentagon is (5 – 2)(180) = 540 

So, what are the five consecutive integers whose total is 540 

 

Start with (1/5) of 540, then add the two integers on both sides. 

 

(1/5)(540) = 108 so the five would be 106, 107, 108, 109, 110 

r

 Apr 1, 2020

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