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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Proving Angle Relationships

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Exercise 11 Page 305

Do the angles form a linear pair? If so, what can you get from this?

Measures: m∠ 9 = 156 and m∠ 10 = 24
Theorem: Supplement Theorem

Practice makes perfect

Notice that ∠ 9 and ∠ 10 form a linear pair.

The Supplement Theorem tells us that they are supplementary angles, and we get the following relation. m∠ 9+m∠ 10 = 180 Now, let's substitute m∠ 9= 3x+12 and m∠ 10= x-24 into this equation and solve for x.

m∠ 9+m∠ 10 = 180

m∠ 9= 3x+12, m∠ 10= x-24

3x+12 + x-24 = 180

▼

Solve for x

Add and subtract terms

4x-12=180

LHS+12=RHS+12

4x=192

.LHS /4.=.RHS /4.

x=48

Finally, we find the measures of ∠ 9 and ∠ 10 by substituting x=48 into their expressions. lll m∠ 9=3x+12 & ⇒ & m∠ 9=3( 48)+12 & & =156 m∠ 10=x-24 & ⇒ & m∠ 10= 48-24 & & =24

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Exercises p.304-307