Exercise 73 Page 530

What is the sum of the measures of two supplementary angles?

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We want to find the value of x. Examining the diagram, we notice that the angles form a linear pair. Recall the Linear Pair Theorem.

Linear Pair Theorem
If two angles form a linear pair, then they are supplementary angles.

Since the angles are supplementary, we know that the sum of their measures should equal 180^(∘). With this information, we can write an equation by adding the smaller angle's measure, setting their sum equal to 180^(∘), and solving for x^(∘).

x^(∘) + x^(∘)-60^(∘) = 180^(∘)

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Solve for x^(∘)

AddTerms

Add terms

2x^(∘)-60^(∘)=180^(∘)

AddEqn

LHS+60^(∘)=RHS+60^(∘)

2x^(∘)=240^(∘)

DivEqn

.LHS /2.=.RHS /2.

x^(∘)=120^(∘)

Our result correspond to B.

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Exercise 73 Page 530

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