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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 10 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^(∘).

27

We are given that the sum of the interior angle measures of a polygon with n sides is 4500 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 4500^(∘). (n-2)* 180^(∘)= 4500^(∘) Let's solve for n.

(n-2)* 180=4500

.LHS /180.=.RHS /180.

n-2=25

LHS+2=RHS+2

n=27

We found that n=27. This means that the polygon with the given measures has 27 sides.