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Angle Pairs

Understand complementary angles as angles whose sum is 90 degrees and supplementary angles as angles whose sum is 180 degrees.

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Angle Pairs

Remember the trip to the art museum from the Angle Classification Concept? Well, previously we worked on identifying different types of angles in the stained glass. Now the students are going to need to identify angle pairs. These angle pairs can also be found in the stained glass. Here is the stained glass once again.

In this Concept, you will learn all about angle pairs. Pay close attention and you will be able to find these pairs at the end of the Concept.

Guidance

When we have two angles together, we can say that we have angle pairs. Sometimes, the measures of these angles add up to form a special relationship. Sometimes they don’t. There are two special angle pair relationships for you to learn about. The first one is called complementary angles and the second one is called supplementary angles.

Complementary angles are two angles whose measurements add up to exactly \begin{align*}90^\circ\end{align*}. 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 @$\begin{align*}180^\circ\end{align*}@$. When we put them together, they form a straight angle. Take a look at the pairs of supplementary angles below.

Let’s practice classifying some pairs of angles.

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

The sum of the angles in Figure 1 is @$\begin{align*}180^\circ\end{align*}@$. Therefore these angles are supplementary angles.

The sum of the angles in Figure 2 is @$\begin{align*}90^\circ\end{align*}@$. Therefore these angles are complementary angles.

Remember, complementary angles add up to @$\begin{align*}90^\circ\end{align*}@$ and supplementary angles add up to @$\begin{align*}180^\circ\end{align*}@$. In order to classify the pairs as complementary or supplementary, we need to add the measures of the angles in each pair together to find out the total.

Now it's your turn to try a few. Identify the angle pairs as complementary, supplementary or neither.

Example A

Angle @$\begin{align*}A = 23^\circ\end{align*}@$, Angle @$\begin{align*}B = 45^\circ\end{align*}@$

Solution: Neither

Example B

Angle @$\begin{align*}A = 45^\circ\end{align*}@$, Angle @$\begin{align*}B = 45^\circ\end{align*}@$

Solution: Complementary

Example C

Angle @$\begin{align*}A = 103^\circ\end{align*}@$, Angle @$\begin{align*}B = 77^\circ\end{align*}@$

Solution: Supplementary

Now that you have learned about angle pairs. Look at the stained glass once again.

Write down or draw a copy of the stained glass in your notebook. Then identify the angle pairs that you can find. When you have done this, discuss your findings with a friend.

Guided Practice

Here is one for you to try on your own.

Are angles @$\begin{align*}X\end{align*}@$ and @$\begin{align*}Y\end{align*}@$ complementary or supplementary?

Answer

The question asks us to classify angles @$\begin{align*}X\end{align*}@$ and @$\begin{align*}Y\end{align*}@$ as either complementary or supplementary. Look at the figure. This time we do not know the measures of any of the angles. Can we still answer the question?

We can. We know that complementary angles add up to @$\begin{align*}90^\circ\end{align*}@$ and supplementary angles add up to @$\begin{align*}180^\circ\end{align*}@$. We also know that @$\begin{align*}90^\circ\end{align*}@$ is a right angle and that @$\begin{align*}180^\circ\end{align*}@$ is a straight angle. Now take a good look at angles @$\begin{align*}X\end{align*}@$ and @$\begin{align*}Y\end{align*}@$. If we put them together as a whole, do they form a right angle or a straight angle? They form a straight angle, so they must be supplementary.

Video Review

This is a James Sousa video on the types of angles.

Explore More

Directions: Identify whether the pairs below are complementary or supplementary or neither.

1.

2.

3.

4. An angle pair whose sum is @$\begin{align*}180^\circ\end{align*}@$

5. Angle @$\begin{align*}A = 90^\circ\end{align*}@$ Angle @$\begin{align*}B\end{align*}@$ is @$\begin{align*}45^\circ\end{align*}@$

6. Angle @$\begin{align*}C = 125^\circ\end{align*}@$ Angle @$\begin{align*}B = 55^\circ\end{align*}@$

7. An angle pair whose sum is @$\begin{align*}180^\circ\end{align*}@$

8. An angle pair whose sum is @$\begin{align*}245^\circ\end{align*}@$

9. An angle pair whose sum is @$\begin{align*}80^\circ\end{align*}@$

10. An angle pair whose sum is @$\begin{align*}90^\circ\end{align*}@$

11. An angle pair whose sum is @$\begin{align*}55^\circ\end{align*}@$

12. An angle pair whose sum is @$\begin{align*}120^\circ\end{align*}@$

13. An angle pair whose sum is @$\begin{align*}95^\circ\end{align*}@$

14. An angle pair whose sum is @$\begin{align*}201^\circ\end{align*}@$

15. An angle pair whose sum is @$\begin{align*}190^\circ\end{align*}@$

Vocabulary

Acute Angle

Acute Angle

An acute angle is an angle with a measure of less than 90 degrees.
Angle Pairs

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

Complementary angles are a pair of angles with a sum of 90^{\circ}.
Degree

Degree

A degree is a unit for measuring angles in a circle. There are 360 degrees in a circle.
Obtuse angle

Obtuse angle

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.
Riemann sum

Riemann sum

A Riemann sum is an approximation of the area under a curve, calculated by dividing the region up into shapes that approximate the space.
Supplementary angles

Supplementary angles

Supplementary angles are two angles whose sum is 180 degrees.

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