Exercise 77 Page 42

Practice makes perfect

a From the diagram, we see that the two angles are vertical angles. This means they have equal measures according to the Vertical Angles Theorem.

Let's solve for x in our equation.

5x-57^(∘)=3x+5^(∘)

SubEqn

LHS-3x=RHS-3x

2x-57^(∘)=5^(∘)

AddEqn

LHS+57^(∘)=RHS+57^(∘)

2x=62^(∘)

DivEqn

.LHS /2.=.RHS /2.

x=31^(∘)

b From the diagram, we see that the angles form a straight angle which means they are supplementary angles. With this, we can write an equation as the measures of supplementary angles sum to be 180^(∘).

Let's solve for x in this equation.

2x+(4x+150^(∘))=180^(∘)

RemovePar

Remove parentheses

2x+4x+150^(∘)=180^(∘)

AddTerms

Add terms

6x+150^(∘)=180^(∘)

SubEqn

LHS-150^(∘)=RHS-150^(∘)

6x=30^(∘)

DivEqn

.LHS /6.=.RHS /6.

x=5^(∘)

Subchapter links

1.3.1 Angle Pair Relationships p.42-43

1.3.2 Angles Formed by Transversals p.48-49

1.3.3 More Angles Formed by Transversals p.53-54

100

101

102

103

1.3.4 More Angles Formed by Transversals p.59-60

110

111

112

113

114

115

Exercise 77 Page 42

Hints

Check the answer

Practice exercises

Asses your skill