Geometry is one of the oldest and important branches of mathematics that deals with the properties of shapes such as lines and angles. Supplementary angles, like vertical and complementary angles, are all pairs of angles.
However, supplementary and complementary angles do not have to be adjacent to each other, unlike vertical angles.
Determining and finding the measures of angles is one of the most commonly performed steps in Geometry. And in order to do so, we need to familiarize ourselves with these geometric terms.
Are you ready to tackle another pair of angles called supplementary angles? Say no more as we dive into another adventure of defining supplementary angles and comparing them to other pairs of angles.
Supplementary angles
Supplementary angles are angles that when added together, their sum is
Let’s look at one example of supplementary angles.
In the figure, we can see two angles – one measuring
Since the sum is exactly
When two angles are supplementary, we call each pair the supplement of the other angle. Hence, in this case,
More so, if you will notice, the two angles formed a straight line. Just like linear pairs, supplementary angles are pairs of angles that can form a straight line because their sum is
Types of Supplementary Angles
Like complementary angles, supplementary angles can be adjacent or nonadjacent. Let’s discuss how these two types are different from each other.
Adjacent Supplementary Angles
If two angles share a common vertex and a common side and have a total of
Let’s take a look at these illustrations.
By observation, we can easily tell that adjacent supplementary angles form a straight line.
Nonadjacent Supplementary Angles
If two angles are nonadjacent but have a total angle measure of
Let’s look at the examples to see how it is different from adjacent supplementary angles.
In the given figure, if two angles do not share the same side or vertex, they can still be supplementary angles as long as the sum of the two angles is
Did you know that…
That the word “supplementary” is from two Latin words, “supplere” and “plere.” Supplere means “supply” while “plere” means “fill.” So we can simply say that “supplementary” means “something to supply to fill a thing.”
And so are the supplements of angles!
How to find the supplement of an angle?
There may be cases or problems that you will encore that will require you to find the other pair of supplementary angles. Are you getting curious about how we can solve these types of problems?
Well, here’s an easy way of solving and finding the supplement of a certain angle!
By definition, we already know that supplementary angles always add up to 180. Hence, if one is already given, we can easily find the supplement of the angle by simply subtracting the angle’s measure from
Say, for example, we have an angle whose measure is
Therefore, the supplement of
It’s simple, right? It is basically subtracting the given angle from
Now, let’s try another example. I
To solve this problem, we will always go back to the definition of supplementary angles. Since the given angle measures
Therefore, by subtraction, we are able to know that the supplement of
See, finding the supplement of a certain is as easy. You just always have to remember the total angle measure of supplementary angles.
Solving problems involving supplementary angles
Now that you know the basics of finding the supplement of specific angles, let’s try to apply it to solve more problems.
Problem 1
Suppose the line formed by two angles is a straight line, as shown in the figure. What should be the angle measure of x?
To find the value of x in the given problem, need to create a mathematical sentence to show that their sum is
To find the value of x, we can rewrite the equation as
Now, let’s try another problem without the aid of illustrations.
Problem 2
If
This may look confusing and difficult to answer, but it’s actually not. To solve this type of problem, we are going to use our knowledge in algebra.
We already know that If
Then, we have a condition wherein
By substituting the
Hence,
Thus, we now know that
Since
Therefore, the angle measure of
Supplementary angles VS Complementary angles
Supplementary and complementary angles are pairs of angles that add up to
Supplementary Angles  Complementary Angles 
The sum of the two angles is

The sum of the two angles is

The supplement of an angle can be solved using the formula

The complement of an angle can be solved using the formula

Supplementary angles form a straight angle when combined together.  Complementary angles form a right angle when combined together. 
Supplementary starts with letter “S” and Straight also starts with letter “S”. Thus, this can be a way to easily remember that a pair of supplementary angles forms a straight line.  Complementary starts with letter “C” and “Corner” also starts with letter “C.” Thus, complementary angles can be remembered as Corner (right) angles when they are combined together. 
Take a quiz
Which of the following is not true about supplementary angles?
 Supplementary angles are also named as linear pairs.
 Supplementary angles are also called as straight angles.
 Supplementary angles are also referred to as complementary angles.
Supplementary angles are also referred to as complementary angles.
What is the supplement of an angle that measures 73?
If A and B are supplementary angles. What are the measures of the two angles if B measures onehalf of A?
Which of the following pairs of angles is not an example of supplementary angles?
Frequently Asked Questions
Supplementary angles are pairs of angles that measure exactly
No, two acute angles cannot be supplementary because the sum of any two angles less than
No, two obtuse angles cannot be supplementary because the sum of any two obtuse angles will always exceed
Yes, two right angles can be supplementary angles because the angle measure of any right angle is
No, supplementary angles can only appear in pairs. Even though the sum of three angles is equal to
No. The pair of complementary angles measure exactly
Yes. Since the sum of supplementary angles is