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9.6: Supplementary and Complementary Angle Pairs

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Remember the skateboard park from the last Concept? Well, the boys were looking at angles, but they could have also looked at angle pairs. Look at the diagram once again.

Are there any supplementary or complementary angle pairs here?

To answer this question, you will need to know how to identify these angle pairs. You will learn that in this Concept.

Guidance

Sometimes, we can have two angles that are a part of each other or are connected to each other. When we have this happen, we call these two angles angle pairs .

Here we are looking at two special types of angle pairs, supplementary angles or complementary angles .

What are supplementary angles?

Supplementary angles are two angles whose sum is equal to 180^\circ . In other words when we add the measure of one angle in the pair with the other angle in the pair, together they equal 180 degrees.

These two angles are supplementary because together they form a straight line. We can also tell that they are supplementary because when we add their angle measures the sum is equal to 180 degrees. 120 + 60 = 180^\circ

Here is a real life example of supplementary angles. Notice that the two streets indicated by the arrows are right angles. Two right angles are equal to 180 degrees. Therefore, this intersection is an example of supplementary angles.

What are complementary angles?

Complementary angles are a pair of angles whose sum is 90^\circ . Here is an example of a two complementary angles.

If we add up the two angle measures, the sum is equal to 90 degrees. Therefore, the two angles are complementary.

You can find missing angle measures by using this information about supplementary and complementary angles.

Find the measure of x .

First, we can identify that these two angles are supplementary. They form a straight line. The total number of degrees in a straight line is 180. Therefore, we can write the following equation to solve.

130 + x & = 180 \\x & = 50^\circ

Our missing angle is equal to 50^\circ .

Here the two angles are complementary. Therefore the sum of the two angles is equal to 90 degrees. We can write an equation and solve for the missing angle measure.

75 + x & = 90 \\x & = 15^\circ

Our missing angle measure is equal to 50^\circ .

It is time to practice. Write whether each pair is complementary or supplementary.

Example A

If the sum of the angles is equal to 180 degrees.

Solution: The angles are supplementary angles.

Example B

If one angle is 60 degrees and the other angle is 120 degrees.

Solution: The angles are supplementary angles.

Example C

If the sum of the angle measures is 90 degrees.

Solution: The angles are complementary.

Now let's go back and look at the original design of the skateboard park. Can you find any supplementary or complementary angles?

By drawing arrows on the school map, we can see where all of the right angles are located. There are eight right angles located on the outside border of the plan for the soccer field. Two of the pairs of right angles in the middle of the field add together to form straight lines. Therefore, we can say that there are two pairs of supplementary angles.

Isaac and Marc can use these angles to create the perfect design for the new school skatepark.

Vocabulary

Here are the vocabulary words in this Concept.

Acute angle
an angle less than 90 degrees.
Right angle
an angle equal to 90 degrees.
Obtuse angle
an angle greater than 90 degrees but less than 180 degrees.
Straight angle
a straight line equal to 180 degrees
Supplementary angles
two angles whose sum is 180 degrees.
Complementary angles
two angles whose sum is 90 degrees.

Guided Practice

Here is one for you to practice on your own.

Identify the following angle pairs as supplementary or complementary.

Answer

The sum of the first pair of angles is 180 degrees. Therefore, the angles are supplementary.

The sum of the second pair of angles is 90 degrees. Therefore, the angles are complementary.

Video Review

Here is a video for review.

James Sousa, Introduction to Angles

James Sousa, Types of Angles

Practice

Directions: Identify each angle pair as supplementary or complementary angles.

1.

2.

3.

4.

Directions: Use what you have learned about complementary and supplementary angles to answer the following questions.

5. If two angles are complementary, then their sum is equal to _________ degrees.

6. If two angles are supplementary, then their sum is equal to ________ degrees.

7. True or false. If one angle is 120^\circ , then the second angle must be equal to 90^\circ for the angles to be supplementary.

8. True or false. If the angles are supplementary and one angle is equal to 100^\circ , then the other angle must be equal to 80^\circ .

9. True or false. The sum of complementary angles is 180^\circ .

10. True or false. The sum of supplementary angles is 90^\circ .

Directions: Identify whether the angles are supplementary, complementary or neither based on the angle measures.

11. One angle is 50 degrees. The other angle is 130 degrees.

12. One angle is 30 degrees. The other angle is 60 degrees.

13. One angle is 112 degrees. The other angle is 70 degrees.

14. One angle is 110 degrees. The other angle is 50 degrees.

15. One angle is 35 degrees. The other angle is 55 degrees.

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Difficulty Level:

Basic

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Date Created:

Oct 29, 2012

Last Modified:

Aug 18, 2014
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