Exercise 14 Page 52

We have been given a pair of supplementary angles and their measures written as algebraic expressions. m∠ EFG=& (3x+17)^(∘) m∠ LMN=& (1/2x-5)^(∘)Since the angles are supplementary, we know that the sum of their measures should equal 180^(∘). We can solve for x by creating an equation using the expressions for the two smaller angles and their sum.

m∠ EFG + m∠ LMN = 180

SubstituteII

m∠ EFG= 3x+17, m∠ LMN= 1/2x-5

( 3x+17) + ( 1/2x-5) = 180

RemovePar

Remove parentheses

3x+17 + 1/2x-5 = 180

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Solve for x

AddSubTerms

Add and subtract terms

3 12x+12 = 180

SubEqn

LHS-12=RHS-12

3 12x = 168

MixedToFrac

a bc=a* c+b/c

6+1/2x=168

AddTerms

Add terms

7/2x=168

MultEqn

LHS * 2=RHS* 2

7x=336

DivEqn

.LHS /7.=.RHS /7.

x=48

Now we can substitute this value of x into the given expressions to find the measures of the angles. m∠ EFG ⇒ & 3( 48)+17=161^(∘) m∠ LMN ⇒ & 1/2( 48)-5=19^(∘)