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?

helpppp Apr 1, 2020

#1**+1 **

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Impasta Apr 1, 2020

#5**0 **

*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**

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Guest Apr 1, 2020