What are Complementary Angles: Definition, Examples, Worksheets

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How to find Complementary Angles in 3 EASY steps (Complementary Angles Definition and Examples)

Key Points about Complementary Angles

  • Complementary angles are pairs of angles that add up to 90 degrees.
  • The complementary angle formula is used to find complementary angles.
  • Complementary angles have many real-world applications in fields such as construction, engineering, and art.

Here’s how to find Complementary Angles

Complementary angles are pairs of angles that add up to 90 degrees. They are an important concept in geometry and have many real-world applications. In order to find complementary angles, one must know how to identify them and use the complementary angle formula.

Complementary angles are often used in real-world situations, such as in construction, engineering, and architecture. They are also used in navigation, astronomy, and even art. Understanding complementary angles is essential for anyone who wants to work in these fields or simply has an interest in geometry.

Complementary Angles are made of up two angles whose sum is 90 degrees. This means that when two angles are added together and their sum is 90 degrees then they are Complementary Angles. You can find out if angles are Complementary Angles by using addition or subtraction. When determining which angles what are Complementary Angles, you subtract to get any missing angles measure. For example, if you know one angle measure is 60 degrees and you need to find out the second angle measure, you can do 90 degrees subtracted by 60 degrees to get the remaining angle measure.

Common Core Standard: 7.G.5
Related Topics: Area of a Circle, Area of a Semicircle, Circumference of a Circle, Perimeter of a Semicircle, Supplementary Angles, Vertical Angles
Return To: Home, 7th Grade

What are Complementary Angles

How to Solve Complementary Angles in 3 Easy Steps

Complementary angles are two angles whose sum equals 90 degrees. To find the complement of an angle, you need to subtract the angle from 90 degrees. Here are a few steps to help you solve for complementary angles:

  1. Identify the angle: First, identify the angle for which you want to find the complement.
  2. Subtract the angle from 90 degrees: Once you have identified the angle, subtract it from 90 degrees. The result will be the complement of the angle.
  3. Check your answer: To check your answer, add the angle and its complement. The sum should be equal to 90 degrees.

If you are given the value of one angle and asked to find its complement, you can use an equation to solve for the unknown angle. For example, if angle A is 40 degrees, then its complement angle B can be found using the equation:

A + B = 90
40 + B = 90
B = 50

Therefore, the complement of angle A is 50 degrees.

In some cases, you may be given the value of the complement and asked to find the angle. To do this, you would need to subtract the complement from 90 degrees. For example, if the complement of angle A is 30 degrees, then angle A can be found using the equation:

A + 30 = 90
A = 60

Therefore, angle A is 60 degrees.

In conclusion, finding complementary angles involves subtracting an angle from 90 degrees or solving an equation with one unknown angle. By following the steps outlined above, you can easily find the complement of any angle or solve for a missing angle.

 

Complementary Angles Formula

Complementary angles are two angles that add up to 90 degrees or 90°. When two angles are complementary, they are said to “complement” each other. Complementary angles are always acute angles, meaning they are less than 90 degrees.

The formula for complementary angles is simple. If two angles are complementary, then the sum of the two angles is equal to 90 degrees. Mathematically, it can be expressed as:

∠A + ∠B = 90°

where ∠A and ∠B are the two complementary angles.

It is important to note that the concept of complementary angles applies only to angles that add up to 90 degrees. Any two angles that do not add up to 90 degrees are not complementary angles.

The concept of complementary angles is widely used in geometry and trigonometry. In geometry, complementary angles are often used to solve problems involving right triangles. In trigonometry, the trigonometric ratios of complementary angles are used to simplify trigonometric expressions and solve trigonometric equations.

Knowing the formula for complementary angles can be helpful in solving problems involving angles. For example, if one angle in a pair of complementary angles is given, the other angle can be easily found by subtracting the given angle from 90 degrees. Similarly, if the sum of two angles is given and it is known that they are complementary, then the two angles can be easily found by solving a simple equation.

In summary, the formula for complementary angles is ∠A + ∠B = 90°, where ∠A and ∠B are the two complementary angles. This concept is widely used in geometry and trigonometry and can be helpful in solving problems involving angles.

 

Complementary Angles Definition in Geometry

Complementary angles are a fundamental concept in geometry that refers to two angles whose measures add up to 90 degrees. The term “complementary” comes from the Latin word “complementum,” meaning “something that completes or makes perfect.” In the case of complementary angles, the sum of their measures completes a right angle, which is a 90-degree angle.

In mathematical terms, if angle A and angle B are complementary, then:

  • The measure of angle A + the measure of angle B = 90 degrees
  • Angle A and angle B are both acute angles (less than 90 degrees)

Complementary angles can be part of the same figure or different figures. They do not need to be adjacent angles or oriented in the same direction. If any two angles sum to exactly 90 degrees, then they are two complementary angles.

When one angle measure is given, complementary angles can be used to find the measure of the missing angle. For example, if angle A measures 40 degrees, then angle B must measure 50 degrees, since 40 + 50 = 90.

It is important to note that complementary angles are not the same as supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees, while complementary angles add up to 90 degrees.

In summary, complementary angles are two angles whose measures add up to 90 degrees, and they are an important concept in geometry. They can be used to find the measure of a missing angle, and they are not the same as supplementary angles.

What are Complementary Angles Solution

4 Simple Complementary Angles Examples

Complementary angles are two angles whose sum is equal to 90 degrees.

  1. Complementary Angles are two angles that add up to 90 degrees.
  2. If you know one angle measure, you subtract it from 90 degrees to get the other angle measure.
  3. You can check to make sure the angles are Complementary Angles by making sure they are Right Angles.

Here are a few examples of complementary angles:

Example 1

In the figure below, angle A and angle B are complementary angles because they add up to 90 degrees.

Example 2

Suppose angle C is 25 degrees. What is the measure of angle D if angle D is complementary to angle C?

Let x be the measure of angle D. Since angle C and angle D are complementary, we know that:

C + D = 90

Substituting the value of C, we get:

25 + x = 90

Solving for x, we get:

x = 65

Therefore, angle D measures 65 degrees.

Example 3

In a right triangle, the two non-right angles are complementary. For example, if one angle in a right triangle measures 30 degrees, then the other angle measures 60 degrees because they add up to 90 degrees.

Example 4

Suppose angle E is 40 degrees. What is the measure of angle F if angle E and angle F are complementary?

Let x be the measure of angle F. Since angle E and angle F are complementary, we know that:

E + F = 90

Substituting the value of E, we get:

40 + x = 90

Solving for x, we get:

x = 50

Therefore, angle F measures 50 degrees.

These examples demonstrate how complementary angles work in different scenarios.

 

5 Quick Complementary Angles Practice Problems

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Complementary Angles Quiz

Click Start to begin the practice quiz!

1 / 5

Find the value of x.

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2 / 5

Find the value of x.

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3 / 5

Find the value of x.

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4 / 5

Find the value of x.

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5 / 5

Find the value of x.

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Your score is

0%

 

Supplementary vs Complementary Angles

Complementary angles and supplementary angles are two types of angles that are commonly used in geometry. Both types of angles are related to each other and can be used to solve various problems.

Complementary Angles

Complementary angles are two angles whose sum is equal to 90°. In other words, when two angles are complementary, they add up to form a right angle. A right angle is a 90° angle, which is also known as a straight angle.

For example, if angle A is 30°, then its complementary angle B is 60°, because 30° + 60° = 90°. Complementary angles are always in the same plane and do not need to be adjacent to each other.

Supplementary Angles

Supplementary angles are two angles whose sum is equal to 180°. In other words, when two angles are supplementary, they add up to form a straight line. A straight line is a 180° angle, which is also known as a straight angle.

For example, if angle C is 120°, then its supplementary angle D is 60°, because 120° + 60° = 180°. Supplementary angles are always in the same plane and do not need to be adjacent to each other.

Key Differences

The key difference between complementary and supplementary angles is the sum of the angles. Complementary angles add up to form a right angle, while supplementary angles add up to form a straight line.

Another difference between the two types of angles is that complementary angles are always in the same plane and do not need to be adjacent to each other, while supplementary angles are also always in the same plane but can be adjacent or non-adjacent to each other.

Here is a table that summarizes the key differences between complementary and supplementary angles:

Complementary AnglesSupplementary Angles
Add up to 90°Add up to 180°
Form a right angleForm a straight line
Not necessarily adjacentCan be adjacent or non-adjacent

Understanding the difference between complementary and supplementary angles is important in geometry, as it can help solve various problems related to angles and shapes.

 

Adjacent Complementary Angles

Adjacent complementary angles are two angles that share a common vertex and a common side, and add up to 90 degrees. They are also sometimes referred to as linear pairs of angles.

In other words, if two angles are adjacent and their sum is 90 degrees, then they are adjacent complementary angles. For example, in the figure below, angles AOB and BOC are adjacent complementary angles.

Adjacent Complementary Angles

Adjacent complementary angles are commonly found in geometric figures. They are particularly useful when solving problems involving angles, such as finding the measure of an unknown angle.

To find the measure of an unknown angle, one can use the fact that adjacent complementary angles add up to 90 degrees. For example, if the measure of angle AOB is 40 degrees, then the measure of angle BOC can be found by subtracting 40 from 90, which gives 50 degrees.

It is important to note that not all adjacent angles are complementary. Two angles are only complementary if their sum is 90 degrees. Therefore, adjacent angles that do not add up to 90 degrees are not complementary.

Overall, understanding adjacent complementary angles is essential in geometry. They are commonly used in problem-solving and can help students better understand the relationships between angles in geometric figures.

 

FAQ about Complementary Angles

What are complement angles examples?

Complementary angles are two angles that add up to 90 degrees. For example, if one angle measures 40 degrees, then its complement would measure 50 degrees. Another example would be if one angle measures 20 degrees, then its complement would measure 70 degrees.

Does complementary angle mean 90?

Yes, complementary angles always add up to 90 degrees. If two angles are complementary, then one angle measures x degrees and the other angle measures (90 – x) degrees.

Can complementary angles be 180?

No, complementary angles cannot be 180 degrees. If two angles add up to 180 degrees, then they are called supplementary angles, not complementary angles.

How do you find the complementary angle of an angle?

To find the complementary angle of an angle, subtract the angle’s measure from 90 degrees. For example, if the angle measures 30 degrees, then its complementary angle would measure (90 – 30) = 60 degrees.

What is a Pair of Complementary Angles?

A pair of complementary angles is two angles that add up to 90 degrees. These angles are called complementary because they complement each other to form a right angle.

How to find complementary angles?

To find complementary angles, you can use the formula 90 – x, where x is the measure of one of the angles. For example, if one angle measures 40 degrees, then its complement would measure (90 – 40) = 50 degrees.

What is the formula for Complementary Angles?

The formula for complementary angles is 90 – x, where x is the measure of one of the angles. This formula can be used to find the complement of any angle.

What do Complementary Angles add up to?

Complementary angles always add up to 90 degrees. This is because a right angle measures 90 degrees, and two complementary angles form a right angle.

 

Complementary Angles Worksheet Video Explanation

Watch our free video on Complementary Angles definition. This video shows how to solve problems that are on our free Complementary Angles worksheets that you can get by submitting your email above.

Watch the free Complementary Angles video on YouTube here: Complementary Angles Definition Video

Video Transcript:

This video is about answering the question what are complementary angles. You can get the 7th grade complementary angles worksheet used in this video for free by clicking on the link in the description below.

How do you answer what is complementary angles? Complementary angles are two angles that when added together will add up to 90 degrees. A 90 degree angle is also referred to as a right angle. It is always shown by a square at the junction of two rays that form an angle. In order to solve for complementary angles, you have to take the angle that you know, in this case let’s say this angle is 30 degrees, and we don’t know this angle. You take the angle that you know, which is 30 degrees, and because the two angles added together have to add up to 90 degrees, all you do is you take 90 degrees subtracted by the angle that you know, which is 30 in this case to get your solution. The angle that we’re missing in this example has to be 60 degrees because the two angles added together have to add up to 90. This would have to be 60.

Now we’re going to do a couple practice problems on our complementary angle worksheet. Let’s jump to number two on our complementary angles worksheet. We already know that complementary angles definition is that when two angles added together add up to 90 degrees. But how to solve complementary angles? We can see that this red square at the bottom means that the two angles make a right angle or an angle that’s 90 degrees. We know that this angle right here is 27 degrees but we do not know this angle but we do know that both of these angles have to add up to 90 degrees. We take our 90 degrees, because both of them have to add up to 90, and we’re going to subtract it by the angle we know which in this case is 27 degrees. When you subtract those two you will get 63 degrees which is going to be our answer. Because we know this is 27 and the two together have to be 90 the only option for this angle is that it’s 63 degrees.

Let’s move on to number four on the complementary angles problems worksheet. Now number four gives us another right angle which automatically means that they’re complementary because we know the complementary angles definition is two angles that add up to 90 degrees. What we can do is we can take the angle that we know which is 40 degrees and we can subtract it from 90. We know the whole thing has to be 90 degrees and we know this part right here is 40 degrees so we’re going to subtract it. Then we do 90 degrees minus 40 degrees and we get 50 degrees. So, this angle must be 50 degrees because the two angles together have to add up to 90.

The last problem that we’re going to do on our complementary angles worksheet is number five. Again, complementary angles definition as two angles that add up to 90 degrees. In the case of number five we know one angle has to be 25 degrees but we don’t know the other angle. That’s what we’re going to figure out. If the two added up have to equal 90 that means that we can subtract 25 from 90 and when you subtract 25 from 90 you will get 65 degrees. So we know that this angle must be 65 degrees.

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Free Complementary Angles Worksheet

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