The measure of three of the numbered angles is
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The measure of three of the numbered angles is 120° . Identify the angles. Explain your reasoning.

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EXAMPLE 1

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Example 1

The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning.

By the Corresponding Angles Postulate, m5=120°. Using the Vertical Angles Congruence Theorem, m4=120°. Because 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m8 = 120°.

EXAMPLE 1

Identify congruent angles

SOLUTION


Example 1

ALGEBRA

Find the value of x.

By the Vertical Angles Congruence Theorem, m4=115°. Lines aand bare parallel, so you can use the theorems about parallel lines.

m4 + (x+5)°

180°

=

115° + (x+5)°

180°

=

Substitute 115° for m4.

x + 120 =

180

x =

60

EXAMPLE 2

Use properties of parallel lines

SOLUTION

Consecutive Interior Angles Theorem

Combine like terms.

Subtract 120 from each side.


Example 1

Use the diagram.

1.

If m 1 = 105°, find m 4, m 5, and m 8. Tell which postulate or theorem you use in each case.

m 4 =

m 5 =

m 8 =

ANSWER

105°

105°

105°

for Examples 1 and 2

GUIDED PRACTICE

Vertical Angles Congruence Theorem.

Corresponding Angles Postulate.

Alternate Exterior Angles Theorem


Example 1

Use the diagram.

2.

If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps.

180

m 7 + m 8 =

m 7

ANSWER

68 + 2x + 4 =

180

2x + 72 =

180

m 3 =

2x =

108

x =

54

for Examples 1 and 2

GUIDED PRACTICE


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