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Warm-Up Angle Relationships

Lesson Goals

Use the relationships to findunknown angle

.

Identify

relationships.

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

adjacent angles angles that share a common ray and a common but do not overlap

complementary angles

two angles whose measures have a sum of degrees

congruent having the measure

linear pair adjacent angles that form a

supplementary angles

two angles whose measures have a sum of degrees

vertical angles opposite congruent angles formed by intersecting lines

Lesson Question

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WK2

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Warm-Up Angle Relationships

Types of Angles

Angles can be classified according to their degree measure.

angle angleright angle straight angle

º

less than 90° equal to 90° greater than 90°

less than 180°

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Angle RelationshipsInstruction

Identify Adjacent Angles

Adjacent angles share a ray and a common vertex.

m∠ABD + m∠DBE = m∠

m∠DBE + m∠EBC = m∠DBC

m∠ABE + m∠ = m∠ABC

m∠ABD + m∠DBC = m∠

2Slide

How many angles can you identify?

∠ABD, , ∠EBC

∠ABE, ∠ABC, A B

CD

E

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Angle RelationshipsInstruction

4Slide

6

Identify Linear Pairs

X

Q

MN

P

Intersecting lines form angles with a

common at the point of

intersection.

∠MXN and ∠NXP are adjacent angles

that form a angle:

m∠MXN + m∠NXP =

Because ∠MXP is a line, the adjacent angles are called a linear pair.

What are some other linear pairs in the diagram?

∠NXP and

and ∠QXM

∠QXM and

Identify Vertical Angles

Which angle pairs are not adjacent?

• Pairs of vertical angles:

∠AMY and

and ∠XMA

• Vertical angles are congruent.

∠AMY ∠XMB

∠YMB ≅

MX

A

Y

B

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Angle RelationshipsInstruction

9Slide

Complementary Angles

Two angles whose measures have a

of 90° are complementary

angles.

60° + 30° =

If complementary angles are adjacent, they form a:

Angle

30° 60°

30°60°

Supplementary Angles

Two angles are supplementary angles if their measures have a sum of 180°.

80° + = 180°

Adjacent supplementary angles form a:

Line

Pair

80° 100°

100° 80°

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Angle RelationshipsInstruction

11Slide

Measures of Angle Pairs

140°

40° 40°140°

X

Q

MN

P

lines form two types of angle relationships.

Adjacent angles

A pair of adjacent angles are linear pairs.

Their measures: add to

Vertical angles

The pair of nonadjacent angles are vertical.

Vertical angles have measures that are:

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Angle RelationshipsInstruction

Apply Angle Relationships

Find the missing angle measures:

m∠CFD = m∠ − 50°

= − 50°= 40°

m∠AFE = m∠BFC + m∠ = 90° + 40°

=

m∠BFA =

Because ∠BFA forms vertical angle pair with ∠DFE.

B

A

50°90°

F

CD

E

Solving Angle Problems in the Real World

The railroad track meets the streets as shown below.

Smith Ave.

Brown Ave.

40°

40°

s

The town will allow a company to build a train stop at angle s if the measure of ∠s is greater than 40°. Can a train stop be built at ∠s?

m∠s = 90° −

=

So the company will be allowed to build a train stop there.

14Slide

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Summary Angle Relationships

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Answer

Review: Key Concepts

Adjacent angles share a common ray and vertex.

Linear pairs are adjacent angles that form a straight .

Vertical angles are opposite congruent angles formed by intersecting lines.

angles sum to 90°.

Supplementary angles sum to 180°.

Lesson Question How can you use angle relationships to find unknown angles?

2

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Summary Angle Relationships

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