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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Angles of Polygons

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Exercise 28 Page 480

The Polygon Interior Angles Sum Theorem says that the sum of the measures of the interior angles of an n -sided convex polygon is (n-2)180.

6

Practice makes perfect

We are given that the measure of an interior angle of a regular n -gon is 120 and we want to find n. 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 that each have a measure 120. Therefore, the sum of the angle measures equals n times 120. (n-2)180 = 120n Let's solve the above equation to find n.

(n - 2)180 = 120n

Distribute 180

180n - 360 = 120n

LHS+360=RHS+360

180n = 120n + 360

LHS-120n=RHS-120n

60n = 360

.LHS /60.=.RHS /60.

n = 6

We found that n=6. This means that the polygon with the given measure of an interior angle has 6 sides.

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Exercises p.479-483