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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 14 Page 532

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.

8

Practice makes perfect

We are given that the measure of an interior angle of a regular n -gon is 135 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 135. Therefore, the sum of the angle measures equals n times 135. (n-2)180 = 135n Let's solve the above equation to find n.

(n - 2)180 = 135n

Distribute 180

180n - 360 = 135n

LHS+360=RHS+360

180n = 135n + 360

LHS-135n=RHS-135n

45n = 360

.LHS /45.=.RHS /45.

n = 8

We found that n=8. This means that the polygon with the given measure of an interior angle has 8 sides.

Subchapter links

1 Angles of Polygons p.532

2 Parallelograms p.532

3 Tests for Parallelograms p.533

4 Rectangles p.533

5 Rhombi and Squares p.534

6 Trapezoids and Kites p.534