6–1 Line and Angle Relationships -...

146 Math Connects, Course 3

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.6–1 Line and Angle Relationships

MAIN IDEA

• Identify special pairs of angles and relationships of angles formed by two parallel lines cut by a transversal.

Vertical angles are angles formed by

intersecting lines. Vertical angles are .

The sum of the measures of supplementary angles

is .

The sum of the measures of complementary angles

is .

BUILD YOUR VOCABULARY (pages 144–145)

EXAMPLE Finding a Missing Angle Measure

The two angles below are supplementary. Find the value of x.

x˚155˚

155 + x = 180 Write an equation.

= Subtract from each side.

x = 25 Simplify.

EXAMPLE Find a Missing Angle Measure

Find the value of x in the fi gure.

Use the two vertical angles to solve 68�

x�

for x.

+ x = Write an equation.

___________ –68 –68 Subtract 68 from each side.

x = Simplify.

KEY CONCEPTS

Acute angles have measures less than 90°.

Right angles have measures equal to 90º.

Obtuse angles have measures between 90° and 180°.

Straight angles have measures equal to 180°.

143-165_CH06_881084.indd 146143-165_CH06_881084.indd 146 11/19/07 10:34:15 AM11/19/07 10:34:15 AM

6–1

Math Connects, Course 3 147

Cop

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ht ©

Gle

ncoe

/McG

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-Hill

, a d

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of T

he M

cGra

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.Check Your Progress Find the value of x in each fi gure.

a. b.

70˚

x˚

Lines that intersect at angles are called

perpendicular lines.

Two lines in a plane that never or cross are

called parallel lines.

A transversal is a line that two or more lines.

Interior angles lie the two lines and exterior

angles lie the two lines.

Alternate interior angles are angles that lie

on opposite sides of the transversal.

Alternate exterior angles are exterior angles that lie on

sides of the transversal.

Corresponding angles are those angles that are in the same

on the two lines in relation to the transversal.

BUILD YOUR VOCABULARY (pages 144–145)


6–1

148 Math Connects, Course 3

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

HOMEWORKASSIGNMENTPage(s):

Exercises:

EXAMPLE Find an Angle Measure

BRIDGES The sketch below shows a simple bridge design. The top beam and the fl oor of the bridge are parallel. If ∠2 � ∠3 and m∠3 = 55°, classify the relationship between ∠1 and ∠5. Then fi nd m∠1 and m∠5.

Since ∠3 and ∠5 are angles, they are

congruent. Also, since ∠1 and ∠2 are ,

∠1 and ∠3 are , and ∠1 and ∠5 are

supplementary.

Since m∠3 = 55° and ∠2 � ∠3, m∠2 = .

Since ∠3 and ∠5 are alternate interior angles, m∠5 = .

Since ∠1 and ∠2 are supplementary, the sum of their measures is 180°.

Therefore, m∠1 = 180° − 55° or .

Check Your Progress BRIDGES The sketch below shows a simple bridge design. The top beam and fl oor of the bridge are parallel. If m∠1 = 45° and m∠3 = 40°, fi nd m∠4.

1 4 2

3

ORGANIZE ITUse sketches and words to defi ne the lines and angles discussed in this lesson. Try to show relationships among different lines and angles. Write this in your Foldable.

®


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