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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Angles of Polygons
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Exercise 19 Page 480

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

m∠ U=60
m∠ V=193
m∠ W=76
m∠ Y=68
m∠ Z=143

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^(∘). (x-8)^(∘)+(3x-11)^(∘)+(x+8)^(∘)+x^(∘)+(2x+7)^(∘) = (n-2)180^(∘) Our polygon has 5 sides, so we can substitute 5 for n and solve our equation to find x.
(x-8)^(∘)+(3x-11)^(∘)+(x+8)^(∘)+x^(∘)+(2x+7)^(∘)=(n-2)180^(∘)
Substitute

n= 5

(x-8)^(∘)+(3x-11)^(∘)+(x+8)^(∘)+x^(∘)+(2x+7)^(∘)=( 5-2)180^(∘)
▼
Solve for x
RemovePar

Remove parentheses

x^(∘)-8^(∘)+3x^(∘)-11^(∘)+x^(∘)+8^(∘)+x^(∘)+2x^(∘)+7^(∘)=(5-2)180^(∘)
AddSubTerms

Add and subtract terms

8x^(∘)-4^(∘)=(5-2)180^(∘)
SubTerm

Subtract term

8x^(∘)-4^(∘)=(3)180^(∘)
Multiply

Multiply

8x^(∘)-4^(∘)=540^(∘)
AddEqn

LHS+4^(∘)=RHS+4^(∘)

8x^(∘)=544^(∘)
DivEqn

.LHS /8.=.RHS /8.

x=68^(∘)
Let's substitute x=68, to calculate measures of angles.
Angle Expression x= 68 Simplified
U (x-8)^(∘) ( 68-8)^(∘) 60^(∘)
V (3x-11)^(∘) (3( 68)-11)^(∘) 193^(∘)
W (x+8)^(∘) ( 68+8)^(∘) 76^(∘)
Y x^(∘) 68^(∘) 68^(∘)
Z (2x+7)^(∘) (2( 68)+7)^(∘) 143^(∘)

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

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arrow_right Exercises p.479-483
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Exercises 2 (Page 479)
Exercises 3 (Page 479)
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