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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 63 Page 627

The Polygon Interior Angles Sum Theorem tells us that the sum of the measures of the interior angles of an n-gon is (n-2)180.

octagon

Practice makes perfect

We are given that the measure of an interior angle of a regular n -gon is 135. The Polygon Interior Angles Sum Theorem tells us that the sum of the interior angle measures of an n-gon is (n-2)180. Since all angles in a regular polygon are congruent, our regular n-gon has n angles with the measure of 135. Thus, the sum of the angle measures equals n times 135. (n-2)180 = 135n Let's solve the above equation to find n. Knowing the value of n we will be able to identify the polygon.

(n-2)180 = 135n

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Solve for n

Distribute 180

180n-360=135n

LHS+360=RHS+360

180n=135n+360

LHS-135n=RHS-135n

45n=360

.LHS /45.=.RHS /45.

n=8

Since the polygon has 8 sides, it is a octagon.

Subchapter links

Exercises p.623-627