6th Grade Math Textbook, Fundamentals

 &KDSWHU

9-3

Key Concept

Complementary Angles

Two angles with a sum of 90 are called.

Each angle is the complementof the other.

complementary angles

Angle Pairs

Objective To identify complementary, supplementary, adjacent, and vertical angles

• To find missing angle measures by solving equations

Alex places a piece of tile, with an angle measuring 36 ,
in one corner of a rectangular backsplash above the kitchen
counter. He needs to place another piece of tile adjacent to
it to complete the square corner. What should the measure
of the angle on the second tile be?

You can classify pairs of angles.

Alex needs a piece of tile with an angle

that is the complement of a 36 angle.

So he needs a piece of tile with an angle

of 90

 36 

 54

.

ABCand DEFare

complementary angles.

32° 58° 90°

C B

A

32°

E

F

D

58°

Key Concept

Supplementary Angles

Two angles with a sum of 180

are called.

Each angle is the supplementof the other.

supplementary angles

Some pairs of angles share a common side and vertex.

MNOand PQRare

supplementary angles.

63° 117° 180°

N O

M

63°

P Q

R

117°

MNOand MNPare

supplementary angles.

63° 117° 180°

O N

M

63°

P

117°

MNOand QRSare

supplementary angles.

63° 117° 180°

O N

M

63°

Q

S

R

117°

ABCand ABDare

complementary angles.

32° 58° 90°

C B

A

D

32°

58°

ABCand FGHare

complementary angles.

32° 58° 90°

C B

A

32°

G H

F

58°

have a common side and

vertex but have no common interior points

(their interior points do not overlap).

1 and 2 are adjacent angles.

Adjacent angles

B

D

A C

12

common

side

Adjacent angles that are supplementary form

a linear pair. Their unshared sides are opposite

rays (rays that form a straight angle).

m 3 m 4 180°

H

EFG

34

common

side