Some things just work better in pairs, like shoes, chopsticks, or headphones. In geometry, some angles also “team up” to form something complete, like a corner or a straight line.
In math, or more precisely, geometry, we call these pairs complementary and supplementary angles.
In this guide, we’ll take a closer look at what complementary and supplementary angles are, how to find them, and where they show up in both diagrams and everyday situations.
We’ll also answer some common questions students ask and give you a chance to practice what you’ve learned with a few try-it-yourself questions.
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An angle is the figure made when two rays start from the same point and go in different directions. That point is called the vertex of the angle.
You can think of it like this: when you open a pair of scissors, the space between the blades forms an angle. The point where the blades are connected is the vertex, and the blades themselves are like the rays.
In math, we label angles with the angle symbol (∠) and measure them in degrees (°). The degree symbol tells us how wide or narrow the angle is.
Based on their measure (in degrees), angles can be sorted into four main types:
Acute Angle: An angle that measures less than 90°
Right Angle: An angle that measures exactly 90°
Obtuse Angle: An angle that measures more than 90° but less than 180°
Straight Angle: An angle that measures exactly 180°
Take a look at the diagram below to see how each type of angle looks when measured.
Angles can be grouped in more than one way.
So far, we’ve looked at them based on how many degrees they measure. But there’s another way to look at angles: how they pair up with other angles.
Two of the most common angle pairs you’ll come across in geometry are called complementary and supplementary angles.
Let’s take a closer look at what they are and how to find them.
But before we proceed, see how Mathnasium’s proprietary teaching approach, the Mathnasium Method™, helps students learn and master any math topic, including complementary and supplementary angles.
Complementary angles are two angles whose measures add up to 90°.
They don’t have to be next to each other. What matters is that their sum is exactly 90°. For example, a 60° angle and a 30° angle are complementary, whether they appear in the same diagram or not.
There are two types of complementary angles:
Adjacent complementary angles: The two angles are next to each other, sharing a side and a vertex. Together, they form a right angle.
Non-adjacent complementary angles: The angles are not connected, but their measures still add up to 90°.
If we know that two angles are complementary, then we know their measures add up to 90 degrees.
That means finding the complement of an angle is as simple as subtracting its measure from 90°.
In other words, if one angle measures x degrees, then its complement is 90° − x.
Let’s say we have an angle that measures 35°. To find its complement, we subtract:
x = 90° − 35°
x = 55°
So, the complement of a 35° angle is 55°.
Pretty simple, right?
Supplementary angles are two angles whose measures add up to 180°.
Just like complementary angles, they don’t need to be connected in a diagram. As long as their measures total 180°, they’re considered supplementary. For example, a 110° angle and a 70° angle are supplementary.
That’s why there are also two types of supplementary angles:
Adjacent supplementary angles: These share a vertex and a side, and together they form a straight line.
Non-adjacent supplementary angles: These are separate angles, but their measures still add up to 180°.
If two angles are supplementary, we know their measures add up to 180 degrees. That means finding the supplement of an angle is just a matter of subtracting its measure from 180°.
In other words, if one angle measures x degrees, then its supplement is 180° − x.
Let’s say one angle measures 112°. To find its supplement, we subtract:
180° − 112° = 68°
So, the complement of a 112° angle is 68°.
And that’s how we find the supplement of an angle.
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Now that we know what both types of angles are, let’s compare them side by side to understand their unique roles in geometry.
The only difference between complementary and supplementary angles is the sum of their measures:
Complementary angles add up to 90° and form a corner.
Supplementary angles add up to 180° and form a straight line.
To tell them apart, you can try to remember this quick word association:
Complementary Corner (90°)
Supplementary Straight line (180°)
Practice makes perfect! Let’s walk through a few step-by-step examples to see how complementary and supplementary angles work in action.
What is the complement of a 56° angle?
We know that complementary angles add up to 90°, so we subtract:
x = 90° − 56°
x = 34°
So, the complement is 34°.
What is the supplement of a 108° angle?
We know that complementary angles add up to 180°, so we subtract:
x = 180° − 108°
x = 72°
The complement of a 108° angle is 72°.
Two angles are complementary, and the difference between them is 22°. What are their measures?
Let the smaller angle be x.
Then the larger angle is x + 22.
Since the angles are complementary:
x + (x + 22) = 90
2x + 22 = 90
2x = 68
x = 34
So, the smaller angle is 34°.
To find the larger angle, we add:
34 + 22 = 56
Finally, the angles are 34° and 56°
Two angles are supplementary, and the difference between them is 58°. What are their measures?
Let the smaller angle be x.
Then the larger angle is x + 58.
Since the angles are supplementary:
x + (x + 58) = 180
2x + 58 = 180
2x = 122
x = 61
So, the smaller angle is 61°.
To find the larger angle, we add:
61 + 58 = 119
Finally, the angles are 61° and 119°.
Let’s see what you remember! Choose the correct answer for each question.
1. Which of the following statements about complementary angles is true?
a) They must always be adjacent.
b) They always form a straight line.
c) They do not have to be next to each other.
d) One angle must be 90°.
2. Which of the following is a pair of supplementary angles?
a) 45° and 45°
b) 60° and 30°
c) 120° and 60°
d) 90° and 45°
3. If two angles are complementary and one measures 26°, what is the other?
a) 74°
b) 66°
c) 64°
d) 84°
4. What do complementary and supplementary angles have in common?
a) Both always form straight lines.
b) Both must be adjacent to each other.
c) Both involve one right angle.
d) Both can be adjacent or non-adjacent.
5. What is the supplement of a 39° angle?
a) 79°
b) 71°
c) 141°
d) 51°
6. Two supplementary angles can both be acute.
a) True
b) False
Learning about complementary and supplementary angles often raises dilemmas.
We've put together a list of questions we hear from students and parents at Mathnasium of Southwest Westminster, along with answers to clear up any confusion.
Most students are introduced to these angle pairs in the 5th or 6th grade, often as part of early geometry or measurement units.
Understanding these relationships helps prepare them for more advanced geometry topics in middle and high school.
No. While they can appear next to each other in a diagram (like forming a right angle or a straight line), they don’t have to.
The key is the total measure—90° for complementary, 180° for supplementary, not their placement.
No. A right angle measures exactly 90°, so two right angles would total 180°, which makes them supplementary, not complementary.
No. An obtuse angle is greater than 90°, and two obtuse angles would always add up to more than 180°. So, at least one of the angles in a pair must be less than 90°, depending on the type of relationship.
You often can’t. You need to know their exact measurements. Unless the diagram is clearly labeled or shows a right or straight angle, don’t assume. Always add the measures to check.
You’ll see these angle pairs in geometry problems involving triangles, quadrilaterals, and parallel lines, as well as in real-world applications like design, architecture, and engineering.
They’re also essential for building reasoning skills in algebra and proofs later on.
Mathnasium of South Westminster is a math-only learning center for K–12 students in Westminster, CO.
Using the Mathnasium Method™, a proprietary teaching approach, our specially trained math tutors provide face-to-face instruction in a caring and engaging group environment. We help students truly understand and enjoy geometry topics, including complementary and supplementary angles, which are often introduced in 5th or 6th-grade math.
Each student begins their Mathnasium enrollment with a diagnostic assessment that helps us identify their strengths, knowledge gaps, and learning style. Based on those insights, we create a personalized learning plan that guides them step-by-step toward math mastery.
Whether your student is just starting to explore angle relationships, needs help with geometry homework, or is preparing for higher-level math, we’re here to help them build confidence and succeed.
Ready to take the first step?
Schedule a Free Assessment at Mathnasium of South Westminster today!
If you've given our quick quiz a try, check your answers here and see how you did!
1. Which of the following statements about complementary angles is true?
c) They do not have to be next to each other
Complementary angles add up to 90°, but they don’t need to be adjacent.
2. Which of the following is a pair of supplementary angles?
Correct answer: c) 120° and 60°
Their sum is 180°, which makes them supplementary.
3. If two angles are complementary and one measures 26°, what is the other?
c) 64°
Because 90° − 26° = 64°
4. What do complementary and supplementary angles have in common?
d) Both can be adjacent or non-adjacent
Angle pairs don’t have to share a side—they just need to satisfy the angle sum.
5. What is the supplement of a 39° angle?
c) 141°
Because 180° − 39° = 141°
6. Two supplementary angles can both be acute.
b) False
Two acute angles are each less than 90°, so they can't add up to 180°.
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