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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 18 Page 480

Use the Polygon Angle-Sum Theorem. How many sides does the polygon have?

m∠ A=m∠ B=90
m∠ C=128
m∠ D=74
m∠ E=158

Practice makes perfect

Let's find the value of x.

Recall the Polygon Angle-Sum Theorem.

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

In this case, expressions are given for the measures of the interior angles. We can write an equation where the sum of these expressions is equal to (n-2)180. 90+90+(2x+10)+x+(2x-20) = (n-2)180 Our polygon has 5 sides, so we can substitute 5 for n and solve our equation to find x.

90+90+(2x+10)+x+(2x-20)=(n-2)180

n= 5

90+90+(2x+10)+x+(2x-20)=( 5-2)180

▼

Solve for x

Remove parentheses

90+90+2x+10+x+2x-20=(5-2)180

Add and subtract terms

5x+170=(5-2)180

Subtract term

5x+170=(3)180

Multiply

5x+170=540

LHS-170=RHS-170

5x=370

.LHS /5.=.RHS /5.

x=74

Let's substitute x=74, to calculate measures of angles.

Angle	Expression	x^(∘)= 74^(∘)	Simplified
C	(2x-20)^(∘)	(2( 74)-20)^(∘)	128^(∘)
D	x^(∘)	74^(∘)	74^(∘)
E	(2x+10)^(∘)	(2( 74)+10)^(∘)	158^(∘)

Now that we have found the measures of all of the angles, we can complete our diagram.

Subchapter links

Exercises p.479-483