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This pdf includes the following topics:-

Recognize complementary and supplementary angles

Supplementary angles

Application of Complementary and Supplementary Angles

Adjacent Angles

Linear Pair

Recognize complementary and supplementary angles

Supplementary angles

Application of Complementary and Supplementary Angles

Adjacent Angles

Linear Pair

1.
2.2 Complementary and Supplementary Angles

Objective: Recognize complementary and supplementary angles

Complementary angles are:

two angles whose sum is 90 degrees (a right angle)

each of the angles is called the complement of the other.

Example 1: If an angle measures 38 degrees, what is its complement?

90 – 38 = x

x = 52

x⁰

38⁰

An illustration indicating the complement to an angle whose measure is also unknown (x):

If the

Then the complement

angle = x x⁰ to angle x =

(90 – x)⁰

The algebraic expression used to represent a complementary angle is

90 - x

Remember! Complements Right Angle Sum 90

Objective: Recognize complementary and supplementary angles

Complementary angles are:

two angles whose sum is 90 degrees (a right angle)

each of the angles is called the complement of the other.

Example 1: If an angle measures 38 degrees, what is its complement?

90 – 38 = x

x = 52

x⁰

38⁰

An illustration indicating the complement to an angle whose measure is also unknown (x):

If the

Then the complement

angle = x x⁰ to angle x =

(90 – x)⁰

The algebraic expression used to represent a complementary angle is

90 - x

Remember! Complements Right Angle Sum 90

2.
Definition

Supplementary angles are:

two angles whose sum is 180 degrees (a straight angle)

each of the two angles is called the supplement of the other

Example 2: If an angle measures 38 degrees, what is the measure of its supplement?

180 – 38 = x

x = 142

x⁰ 38⁰

An illustration indicating the supplement of an angle whose unknown measure = x:

If the Then the supplement

angle = x to angle x =

x⁰ (180 – x)⁰

The algebraic expression used to represent a supplementary angle is:

180 – x

Remember! Supplements Straight Angle Sum 180

To keep from confusing the two, the following logic may help you remember:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

180

90 135

C comes before S in the alphabet, like

90 comes before 180 on a number line!

Supplementary angles are:

two angles whose sum is 180 degrees (a straight angle)

each of the two angles is called the supplement of the other

Example 2: If an angle measures 38 degrees, what is the measure of its supplement?

180 – 38 = x

x = 142

x⁰ 38⁰

An illustration indicating the supplement of an angle whose unknown measure = x:

If the Then the supplement

angle = x to angle x =

x⁰ (180 – x)⁰

The algebraic expression used to represent a supplementary angle is:

180 – x

Remember! Supplements Straight Angle Sum 180

To keep from confusing the two, the following logic may help you remember:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

180

90 135

C comes before S in the alphabet, like

90 comes before 180 on a number line!

3.
Application of Complementary and Supplementary Angles

Example 3: Problem Solving: If the supplement of an angle is 4 times the measure of its

complement, what is the measure of the

angle? Name Expression Measure

The Angle x

Step 1: Make a table and a diagram! Complement 90 – x

Supplement 180 - x

90 - x 180 - x

x

Step 2: Use the expressions in the table above to help you translate the problem into an

the supplement of an angle is 4 times the measure of its complement

180 - x = 4( 90 – x)

Step 3: Now we have this equation from our second table: 180 – x = 4(90 – x)

solve algebraically

180 – x = 4(90 – x)

180 – x = 360 – 4x (distributed the 4)

3x = 180 (added 4x to each side, and subtracted 180 from each side)

x = 60 (divided both sides by 3)

This solution means “the angle” has a measure of 60 degrees.

Step 4: Fill in the last column of table and answer the question! Sometimes you are asked for

the measure of the complement or supplement, so make sure you re-read the question after finding

all three measures!

What is the measure of the angle? 60!

Name Expression Measure

The Angle x 60

Complement 90 – x 30

Supplement 180 - x 120

Example 3: Problem Solving: If the supplement of an angle is 4 times the measure of its

complement, what is the measure of the

angle? Name Expression Measure

The Angle x

Step 1: Make a table and a diagram! Complement 90 – x

Supplement 180 - x

90 - x 180 - x

x

Step 2: Use the expressions in the table above to help you translate the problem into an

the supplement of an angle is 4 times the measure of its complement

180 - x = 4( 90 – x)

Step 3: Now we have this equation from our second table: 180 – x = 4(90 – x)

solve algebraically

180 – x = 4(90 – x)

180 – x = 360 – 4x (distributed the 4)

3x = 180 (added 4x to each side, and subtracted 180 from each side)

x = 60 (divided both sides by 3)

This solution means “the angle” has a measure of 60 degrees.

Step 4: Fill in the last column of table and answer the question! Sometimes you are asked for

the measure of the complement or supplement, so make sure you re-read the question after finding

all three measures!

What is the measure of the angle? 60!

Name Expression Measure

The Angle x 60

Complement 90 – x 30

Supplement 180 - x 120

4.
Other definitions useful for this section:

Opposite Rays-

Two rays with the same endpoint that extend in opposite directions and make up a straight line.

A

C A B

A

A B C A

Adjacent Angles –

Two angles that share a common vertex and a side but do not have any interior points in common.

∡BAD and ∡CAD

∡BAC and ∡CAD are NOT adjacent

share vertex A and side AD with because their interiors overlap!

no common interior points . . .

So they ARE adjacent angles

Linear Pair –

A linear pair of angles are two adjacent angles whose outside rays form a straight angle (line).

∡BAD and ∡CAD are a linear pair!

Psssst… Side Bar!

By the way, you know or have figured out what adjacent means, right?

If not … it means: “next to” or as the problems state it; “sharing a side.”

Now look at the illustrations again with that in mind!

Opposite Rays-

Two rays with the same endpoint that extend in opposite directions and make up a straight line.

A

C A B

A

A B C A

Adjacent Angles –

Two angles that share a common vertex and a side but do not have any interior points in common.

∡BAD and ∡CAD

∡BAC and ∡CAD are NOT adjacent

share vertex A and side AD with because their interiors overlap!

no common interior points . . .

So they ARE adjacent angles

Linear Pair –

A linear pair of angles are two adjacent angles whose outside rays form a straight angle (line).

∡BAD and ∡CAD are a linear pair!

Psssst… Side Bar!

By the way, you know or have figured out what adjacent means, right?

If not … it means: “next to” or as the problems state it; “sharing a side.”

Now look at the illustrations again with that in mind!