Question #223285

A polygon has (2n+5) sides. The sum of the interior angles of the polygon is ?


1
Expert's answer
2021-10-25T16:05:14-0400

The sum of the interior angles of a convex polygon is equal to (m2)180°(m - 2)\cdot180\degree where mm is the number of sides.

Given m=2n+5.m=2n+5.

Then the sum of the interior angles of a convex polygon is equal to

(m2)180°=(2n+52)180°(m - 2)\cdot180\degree=(2n+5 - 2)\cdot180\degree

=(2n+3)180°=(2n+3)\cdot180\degree


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