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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 7 Page 504

The Polygon Angle-Sum Theorem says that the sum of the measures of the interior angles of an n -gon is (n-2)* 180^(∘).

6

We are given that the sum of the interior angle measures of a polygon with n sides is 720^(∘) and we want to find n. Recall the Polygon Angle-Sum Theorem.

Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of a regular n -gon is given by: (n-2)* 180^(∘)

In this case, the sum of the measures of the interior angles is 720. (n-2)* 180^(∘)= 720^(∘) Let's solve for n.

(n-2)* 180=720

.LHS /180.=.RHS /180.

n-2=4

LHS+2=RHS+2

n=6

We found that n=6. This means that the polygon with the given measures has 6 sides.