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# Supplementary and Complementary Angle Pairs

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Practice Supplementary and Complementary Angle Pairs
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Identify Angle Pairs

Have you ever built a model of a house? Take a look at this dilemma.

In Mrs. Patterson’s World Cultures class the students have just started studying house building. Mrs. Patterson explained that house building doesn’t just pertain to the kinds of houses that we live in, but to houses around the world both past and present. The students are going to work on a project on a specific type of house.

Jaime is very excited. She has always been interested in Native Americans, so she has chosen to work on a tipi. Jaime selected one of the books that Mrs. Patterson brought in and began to leaf through the pages looking at all of the different types of tipis constructed.

“Tipis?” Mrs. Patterson asked looking over Jaime’s shoulder.

“Yes, I want to design and build one for part of my project,” Jaime explained.

“That’s wonderful. You will need to use a lot of math to accomplish that too,” Mrs. Patterson stated.

Jaime hadn’t thought about the math involved in building a tipi. But as she looked through the pages on designing and building tipis, she noticed that there were a lot of notes on different angles.

One of the types of angles mentioned was a complementary pair of angles. Another was a supplementary pair of angles. These angles were important to figure out when stitching the liner of the tipi together.

Jaime is puzzled. She can’t remember how to identify a complementary or a supplementary pair of angles.

Pay attention and this Concept will teach you all about angle pairs.

### Guidance

An angle is measurement of the space created when lines intersect. Here is a diagram that shows the angles formed when two lines intersect. You can see that there are four angles created in this drawing and that they are labeled 1 – 4.

We have reviewed some lines and that angles are created when lines intersect. Sometimes, the way that the lines intersect can create an angle pair . This is when two special angles are formed and these angles have a special relationship. Let’s look at some angle pairs.

The two basic forms of angle pairs are called complementary and supplementary angles.

Complementary angles are two angles whose measurements add up to exactly $90^{\circ}$ . In other words, when we put them together they make a right angle. Below are some pairs of complementary angles.

Supplementary angles are two angles whose measurements add up to exactly $180^{\circ}$ . When we put them together, they form a straight angle. A straight angle is a line.

Take a look at the pairs of supplementary angles below.

Once you know how to identify the angle pairs, you will be able to classify angle pairs as supplementary, complementary or neither.

Take a look at this situation.

Classify the following pairs of angles as either complementary or supplementary.

Now let’s look at how we can identify the angle pairs.

First, look at the first pair of angles labeled $a$ . We can see that the measure of the angles in this pair is 30 and 60 degrees. We know that the sum of complementary angles is $90^{\circ}$ . Therefore, we can identify this angle pair as complementary angles.

Now look at the second angle pair labeled $b$ . We can see that the measure of the angles in this pair is 110 and 70. The sum of these two angles is $180^{\circ}$ . These angles are supplementary angles.

Note: The word “supplementary” or “complementary” refers to the relationship between the two angles.

Sometimes, a pair of angles will be neither complementary nor supplementary. Take a look.

The sum of these angles is $70^{\circ}$ . 70 is not 90 nor is it 180, so this angle pair is neither complementary nor supplementary.

Go back and write all of the vocabulary words from this section in your notebooks. Draw a small example of each word next to its definition.

Based on each description, define whether the angle pairs are supplementary, complementary or neither.

#### Example A

A pair of angles whose sum is $130^{\circ}$ .

Solution: Neither

#### Example B

A pair of angles whose sum is $90^{\circ}$ .

Solution: Complementary

#### Example C

A pair of angles whose sum has the same measure as a straight line.

Solution: Supplementary

Now let's go back to the dilemma from the beginning of the Concept.

Jaime needs to understand the difference between complementary and supplementary angle pairs. First, notice that the word “pair” refers to two, so we are talking about two angles.

### Vocabulary

Angle
A geometric figure formed by two rays that connect at a single point or vertex.
Straight angle
A straight angle is a straight line equal to $180^{\circ}$ .
Angle Pairs
An angle pair is composed of two angles whose sum may add up to 180 degrees or 90 degrees.
Complementary Angles
Complementary angles are a pair of angles with a sum of $90^{\circ}$ .
Supplementary Angles
Supplementary angles are two angles whose sum is 180 degrees.

### Guided Practice

Here is one for you to try on your own.

Look at this diagram and identify the pairs of angles that are supplementary.

Solution

First, you must know that supplementary angles are equal to $180^{\circ}$ and also these angle pairs form a straight line.

Now let's look at the diagram.

The following angle pairs are supplementary.

1 and 2

2 and 3

1 and 4

4 and 3

These angle pairs are the solution.

### Explore More

Directions: If the following angle pairs are complementary, then what is the measure of the missing angle?

1. $\angle{A}&=55^{\circ}\\\angle{B}&= ?$
2. $\angle{C}&=33^{\circ}\\\angle{D}&= ?$
3. $\angle{E}&=83^{\circ}\\\angle{F}&= ?$
4. $\angle{G}&=73^{\circ}\\\angle{H}&= ?$

Directions: If the following angle pairs are supplementary, then what is the measure of the missing angle?

1. $\angle{A}&=10^{\circ}\\\angle{B}&= ?$
2. $\angle{A}&=80^{\circ}\\\angle{B}&= ?$
3. $\angle{C}&=30^{\circ}\\\angle{F}&= ?$
4. $\angle{D}&=15^{\circ}\\\angle{E}&= ?$
5. $\angle{M}&=112^{\circ}\\\angle{N}&= ?$
6. $\angle{O}&=2^{\circ}\\\angle{P}&= ?$

Directions: Answer True or False for each of the following questions.

1. Complementary angles are equal to $180^{\circ}$ .
2. Complementary angles are equal to $90^{\circ}$ .
3. Supplementary angles are equal to $90^{\circ}$ .
4. Supplementary angles are equal to $180^{\circ}$ .
5. Angle pairs less than 90 degrees are neither supplementary nor complementary.