6–1 Line and Angle Relationships - Weebly

6?1 Line and Angle Relationships

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

MAIN IDEA

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

KEY CONCEPTS

Acute angles have measures less than 90?.

Right angles have measures equal to 90?.

Obtuse angles have measures between 90? and 180?.

Straight angles have measures equal to 180?.

BUILD YOUR VOCABULARY (pages 144?145)

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

.

EXAMPLE Finding a Missing Angle Measure The two angles below are supplementary. Find the value of x.

x? 155?

155 + x = 180

= x = 25

Write an equation.

Subtract Simplify.

from each side.

EXAMPLE Find a Missing Angle Measure

Find the value of x in the figure.

Use the two vertical angles to solve for x.

68 x

+ x = __ ?6_ 8 _____?_68__

Write an equation. Subtract 68 from each side.

x =

Simplify.

146 Math Connects, Course 3

6?1

Check Your Progress Find the value of x in each figure.

a.

b.

xx X

70? x?

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

BUILD YOUR VOCABULARY (pages 144?145)

Lines that intersect at perpendicular lines.

angles are called

Two lines in a plane that never called parallel lines.

or cross are

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 on opposite sides of the transversal.

angles that lie

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.

Math Connects, Course 3 147

6?1

?

ORGANIZE IT

Use sketches and words to define the lines and angles discussed in this lesson. Try to show relationships among different lines and angles. Write this in your Foldable.

,INEAND !NGLE 2ELATIONSHIPS

EXAMPLE Find an Angle Measure

BRIDGES The sketch below shows a simple bridge design. The top beam and the floor of the bridge are parallel. If 2 3 and m3 = 55?, classify the relationship between 1 and 5. Then find m1 and m5.

Since 3 and 5 are

angles, they are

congruent. Also, since 1 and 2 are

,

1 and 3 are supplementary.

, and 1 and 5 are

Since m3 = 55? and 2 3, m2 =

.

Since 3 and 5 are alternate interior angles, m5 =

.

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

Therefore, m1 = 180? - 55? or

.

Check Your Progress BRIDGES The sketch below shows a simple bridge design. The top beam and floor of the bridge are parallel. If m1 = 45? and m3 = 40?, find m4.

3 14 2

HOMEWORK ASSIGNMENT

Page(s): Exercises:

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

148 Math Connects, Course 3

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