Answer: Sometimes, two angles are a part of each other or are connected to each other. These angles are called angle pairs.
Let's look at two special types of angle pairs, supplementary angles or complementary angles.
Supplementary angles are two angles whose sum is equal to 180∘. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees.
These two angles are supplementary because together they form a straight line. You can also tell that they are supplementary because when you add their angle measures the sum is equal to 180 degrees.
120+60=180∘
Complementary angles are a pair of angles whose sum is 90∘. Here is an example of complementary angles.
If you 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 information about supplementary and complementary angles.
Let's look at an example.
Find the measure of x.
First, identify that these two angles are supplementary. They form a straight line. The total number of degrees in a straight line is 180. Therefore, you can write the following equation to solve.
130+xx=180=50∘
The missing angle is equal to 50∘.
Here the two angles are complementary. Therefore the sum of the two angles is equal to 90 degrees. Write an equation and solve for the missing angle measure.
75+xx=90=15∘
The missing angle measure is equal to 50∘.
Examples
Example 1
Earlier, you were given a problem about Paul and the house.
He has an angle pair that is formed by two 90 degree angles. What type of angle pair is formed when two 90 degree angles are combined?
First,add the two angles to calculate their sum.
90 + 90 = 180
Then, identify which angle pair adds up to 90 degrees.
Supplementary angles
The answer is that the pair are supplementary angles.
Example 2
Identify the angle pair as complementary or supplementary.
First, add the two angles to calculate their sum.
75 + 105 = 180
Then, identify which angle pair adds up to 180 degrees.
Supplementary angles
The answer is supplementary angles.
Write whether each pair is complementary or supplementary.
Example 3
Identify the angle pair as complementary or supplementary.
If the sum of the angles is equal to 180 degrees.
First, identify which angle pair adds up to 180 degrees.
Supplementary angles
The answer is supplementary angles.
Example 4
Identify the angle pair as complementary or supplementary.
If one angle is 60 degrees and the other angle is 120 degrees.
First, add the two angles together to find the sum.
60 + 120 = 180
Then, identify which angle pair adds up to 180 degrees.
Supplementary angles
The answer is supplementary angles.
Example 5
Identify the angle pair as complementary or supplementary.
First, add the two angles to calculate their sum.
30 + 60 = 90
Then, identify which angle pair adds up to 90 degrees.
Complementary angles
The answer is that the pair are complementary angles.
Step-by-step explanation:
