8.2: Angle Pairs
Remember the trip to the art museum? Well, in the last Concept, you practiced 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*}
Supplementary angles are two angles whose measurements add up to exactly \begin{align*}180^\circ\end{align*}
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*}
The sum of the angles in Figure 2 is \begin{align*}90^\circ\end{align*}
Remember, complementary angles add up to \begin{align*}90^\circ\end{align*}
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*}
Solution: Neither
Example B
Angle \begin{align*}A = 45^\circ\end{align*}
Solution: Complementary
Example C
Angle \begin{align*}A = 103^\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.
Vocabulary
Here are the vocabulary words in this Concept.
 Acute Angle

an angle whose measure is less than \begin{align*}90^\circ\end{align*}
90∘
 Obtuse Angle

an angle whose measure is greater than \begin{align*}90^\circ\end{align*}
90∘
 Right Angle

an angle whose measure is equal to \begin{align*}90^\circ\end{align*}
90∘
 Straight Angle

an angle whose measure is equal to \begin{align*}180^\circ\end{align*}
180∘
 Degrees
 how an angle is measured
 Angle Pairs
 when the measures of two angles are added together to form a special relationship
 Supplementary Angles

angle pairs whose sum is \begin{align*}180^\circ\end{align*}
180∘
 Complementary Angles

angle pairs whose sum is \begin{align*}90^\circ\end{align*}
90∘
Guided Practice
Here is one for you to try on your own.
Are angles \begin{align*}X\end{align*}
Answer
The question asks us to classify angles \begin{align*}X\end{align*}
We can. We know that complementary angles add up to \begin{align*}90^\circ\end{align*}
Video Review
Here is a video for review.
 This is a James Sousa video on the types of angles.
Practice
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*}
6. Angle \begin{align*}C = 125^\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*}
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Acute Angle
An acute angle is an angle with a measure of less than 90 degrees.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 .Degree
A degree is a unit for measuring angles in a circle. There are 360 degrees in a circle.Obtuse angle
An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.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 are two angles whose sum is 180 degrees.Image Attributions
Here you'll learn to identify angle pairs as supplementary, complementary or neither.