Holt CA Course 1

9-3 Angle Relationships

MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

California Standards

Holt CA Course 1

9-3 Angle Relationships

Vocabulary

vertical anglesadjacent anglescomplementary anglessupplementary angles

Holt CA Course 1

9-3 Angle Relationships

Angles are congruent if they have the same measure.

Adjacent angles are two angles that are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.

MRN and NRQ are adjacent angles. They share vertex R and RN.

NRQ and QRP are adjacent angles. They share vertex R and RQ.

Holt CA Course 1

9-3 Angle Relationships

Vertical angles are two angles that are formed by two intersecting lines and are not adjacent. Vertical angles have the same measure, so they are always congruent.

MRP and NRQ are vertical angles.

MRN and PRQ are vertical angles.

Holt CA Course 1

9-3 Angle RelationshipsAdditional Example 1: Identifying Adjacent and

Vertical Angles

Tell whether the numbered angles are adjacent or vertical.

A.

5 and 6 are opposite each other and are formed by two intersecting lines.

They are vertical angles.

5 6

Holt CA Course 1

9-3 Angle Relationships

Additional Example 1: Identifying Adjacent and Vertical Angles

Tell whether the numbered angles are adjacent or vertical.

B. 7 and 8 are side by side and have a common vertex and ray.

They are adjacent angles.

7 8

Holt CA Course 1

9-3 Angle Relationships

Check It Out! Example 1

Tell whether the numbered angles are adjacent or vertical.

A.3 and 4 are side by side and have a common vertex and ray.

They are adjacent angles.

3

4

Holt CA Course 1

9-3 Angle RelationshipsCheck It Out! Example 1

Tell whether the numbered angles are adjacent or vertical.

B.

7 and 8 are opposite each other and are formed by two intersecting lines.

They are vertical angles.

7

8

Holt CA Course 1

9-3 Angle Relationships

65° + 25° = 90°

LMN and NMP are complementary.

Complementary angles are two angles whose measures have a sum of 90°.

P

N

M

L

25°65°

Holt CA Course 1

9-3 Angle Relationships

Supplementary angles are two angles whose measures have a sum of 180°.

65° + 115° = 180°

GFE and HJK are supplementary.

K

E

F

115°65°

G

H

J

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Additional Example 2: Identifying Complementary and Supplementary Angles

A. OMP and PMQ

Since 60° + 30° = 90°, PMQ and OMP are complementary.

O

N

P Q

RM

To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mOMP = 75° – 15° = 60°.

Holt CA Course 1

9-3 Angle Relationships

If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle you are measuring is acute, its measure is less than 90°.

Reading Math

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Additional Example 2: Identifying Complementary and Supplementary Angles

B. NMO and OMR

mNMO = 15° and mOMR = 165°

O

N

P Q

RM

Since 15° + 165° = 180°, NMO and OMR are supplementary.

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Additional Example 2: Identifying Complementary and Supplementary Angles

C. PMQ and QMR

Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary.

To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mQMR = 75°.

O

N

P Q

RM

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out! Example 2

A. BAC and CAF

mBAC = 35° and mCAF = 145°

C

B

D

E

FA

Since 35° + 145° = 180°, BAC and CAF are supplementary.

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out! Example 2

B. CAD and EAF

Since 55° + 35° = 90°, CAD and EAF are complementary.

C

B

D

E

F

A

To find mCAD, start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° – 35° = 55°. mEAF = 35°.

Holt CA Course 1

9-3 Angle Relationships

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out! Example 2

C. BAC and EAF

mBAC = 35° and mEAF = 35°

C

B

D

E

FA

Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.