What are Supplementary Angles Definition, Examples, Worksheets

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How to solve Supplementary Angles in 3 EASY steps (Supplementary Angles Examples)

Key Points about Supplementary Angles

  • Supplementary angles are two angles that add up to 180 degrees.
  • Supplementary angles are commonly used in architecture, engineering, and construction to ensure accurate angles and measurements.
  • Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees.

How to find Supplementary Angles

Supplementary angles are two angles that add up to 180 degrees. They are a fundamental concept in geometry and can be found in various real-life scenarios. Supplementary angles are commonly used in architecture, engineering, and construction to ensure accurate measurements and angles.

To find supplementary angles, you need to add the measures of two angles together. If the sum of two angles equals 180 degrees, they are supplementary angles. Supplementary angles are also used to find missing angles in geometric figures.

Complementary angles are another type of angle that is often confused with supplementary angles. Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees. Understanding the difference between these two types of angles is essential in geometry.

Supplementary Angles are two angles whose sum is 180 degrees. This means that when two angles are added together and their sum is 180 degrees then they are Supplementary Angles. You can find out if angles are Supplementary Angles by using addition or subtraction. When determining which angles what are Supplementary Angles, you subtract the angle you know from 180 degrees to get the missing angle 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 180 degrees subtracted by 60 degrees to get the remaining angle measure of 130.

Common Core Standard: 7.G.5
Related Topics: Area of a Circle, Area of a Semicircle, Circumference of a Circle, Perimeter of a Semicircle, Complementary Angles, Vertical Angles
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What are Supplementary Angles

How to Find Supplementary Angles in 5 Easy Steps

Supplementary angles are a pair of angles that add up to 180 degrees. They are commonly used in geometry, physics, and other fields. Here are some steps to find supplementary angles:

  1. Identify the given angle: The first step is to identify the angle that is given in the problem. This angle is usually labeled with a letter or a symbol.
  2. Assign a variable: The next step is to assign a variable to the unknown angle. This variable is usually denoted with a letter or a symbol. Let’s call this angle x.
  3. Write an equation: The sum of the given angle and the unknown angle is 180 degrees. Therefore, you can write an equation like this: given angle + unknown angle = 180 degrees.
  4. Solve for the unknown angle: You can solve for the unknown angle by subtracting the given angle from 180 degrees. The resulting value is the measure of the unknown angle.
  5. Check your answer: Finally, you should check your answer by adding the given angle and the unknown angle. The sum should be equal to 180 degrees.

Here is an example problem to illustrate these steps:

Find the measure of the supplementary angle to an angle of 50 degrees.

  1. Given angle = 50 degrees.
  2. Let x be the unknown angle.
  3. The sum of the given angle and the unknown angle is 180 degrees. Therefore, we can write the equation: 50 + x = 180.
  4. Solving for x, we get: x = 130 degrees.
  5. Checking our answer, we add 50 and 130 degrees, which gives us 180 degrees. Therefore, our answer is correct.

In summary, finding supplementary angles involves identifying the given angle, assigning a variable to the unknown angle, writing an equation, solving for the unknown angle, and checking your answer. By following these steps, you can easily find the supplementary angle to any given angle.

 

Supplementary Angles Definition

Supplementary angles are a pair of angles that add up to 180°. When two angles are supplementary, they form a straight line. The measure of one angle is the supplement of the other angle.

The definition of supplementary angles is an important concept in geometry. It is used to describe the relationship between two angles that add up to 180°. Supplementary angles are often denoted by the symbol ∠, which represents an angle.

One of the properties of supplementary angles is that they are always in the same plane. This means that they are either both vertical angles or both adjacent angles. When two angles are vertical, they share a common vertex and their sides are opposite rays. When two angles are adjacent, they share a common side and their vertices are at the endpoints of that side.

To find the measure of supplementary angles, you can use the property that the sum of their measures is 180°. For example, if one angle measures 120°, the other angle must measure 60° to be supplementary.

In summary, supplementary angles are a pair of angles that add up to 180° and form a straight line. They have several properties, including being in the same plane and having measures that sum to 180°. To find supplementary angles, you can use the property that their measures add up to 180°.

 

Complementary Angles and Supplementary Angles

Complementary angles are two angles whose sum equals 90 degrees. For example, if one angle measures 30 degrees, then the other angle must measure 60 degrees in order for them to be complementary. Complementary angles are often found in right triangles, where one angle is a right angle measuring 90 degrees.

Supplementary angles, on the other hand, are two angles whose sum equals 180 degrees. For example, if one angle measures 60 degrees, then the other angle must measure 120 degrees in order for them to be supplementary. Supplementary angles are often found in parallel lines cut by a transversal, where the angles on the same side of the transversal add up to 180 degrees.

It is important to note that complementary angles do not have to be adjacent, meaning they do not have to share a common side or vertex. However, supplementary angles must be adjacent, meaning they must share a common side and vertex.

Another way to think about complementary and supplementary angles is to use the idea of a “missing angle.” For example, if two angles are complementary and one angle measures 40 degrees, then the missing angle must measure 50 degrees in order for them to add up to 90 degrees. Similarly, if two angles are supplementary and one angle measures 120 degrees, then the missing angle must measure 60 degrees in order for them to add up to 180 degrees.

In summary, complementary angles and supplementary angles are two types of angle pairs that are commonly found in geometry. Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees. Complementary angles do not have to be adjacent, but supplementary angles must be adjacent.

 

What are Supplementary Angles Solution

3 Simple Supplementary Angles Examples 

Supplementary angles are two angles that add up to 180 degrees.

  1. Supplementary Angles are two angles that add up to 180 degrees.
  2. If you know one angle measure, you subtract it from 180 degrees to get the other angle measure.
  3. You can check to make sure angles are Supplementary by making sure the angles form a straight line.

Here are some examples of supplementary angles:

  • Angle A is 120 degrees, and angle B is 60 degrees. Angle A + Angle B = 180 degrees.
  • Angle C is 30 degrees, and angle D is 150 degrees. Angle C + Angle D = 180 degrees.
  • Angle E is 100 degrees, and angle F is 80 degrees. Angle E + Angle F = 180 degrees.

Supplementary angles can also be adjacent angles, which means they share a common side and vertex. Examples of adjacent supplementary angles include:

  • Angle G and angle H are adjacent angles. Angle G measures 110 degrees, and angle H measures 70 degrees. Angle G + Angle H = 180 degrees.
  • Angle I and angle J are adjacent angles. Angle I measures 150 degrees, and angle J measures 30 degrees. Angle I + Angle J = 180 degrees.

In addition to adjacent angles, non-adjacent angles can also be supplementary. For example:

  • Angle K and angle L are non-adjacent angles. Angle K measures 140 degrees, and angle L measures 40 degrees. Angle K + Angle L = 180 degrees.
  • Angle M and angle N are non-adjacent angles. Angle M measures 160 degrees, and angle N measures 20 degrees. Angle M + Angle N = 180 degrees.

Knowing that two angles are supplementary can be helpful in solving geometry problems. For example, if you know that two angles are supplementary and you know the measure of one of the angles, you can use subtraction to find the measure of the other angle.

 

5 Quick Supplementary Angles Practice Problems

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Supplementary Angles Quiz

Click Start to begin the practice quiz!

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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

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Applying Supplementary Angles in Real Life

In Real World Scenarios

Supplementary angles have a wide range of applications in real life scenarios. For instance, in construction, supplementary angles are used to measure the slope of a roof or the angle at which a wall is built. Additionally, supplementary angles are used in the design of bridges, tunnels, and other structures. Engineers use supplementary angles to determine the angles at which beams and columns should be placed to ensure that the structure is stable.

In addition, supplementary angles are used in navigation. Pilots and sailors use angles to determine their position relative to a landmark or other point of reference. They use supplementary angles to calculate the distance between two points and the angle at which they need to travel to reach their destination.

In Mathematical Problems

Supplementary angles are also used in mathematical problems. They are often used to find the measure of an unknown angle. For example, if two angles are supplementary and one of them measures 45°, then the other angle must measure 135°.

Supplementary angles are also used in problems involving parallel lines and a transversal. When a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the alternate exterior angles are congruent. Additionally, the interior angles on the same side of the transversal are supplementary.

Supplementary angles are also used in problems involving parallelograms. The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary.

In addition, supplementary angles are used to find the measure of a corner or an interior angle of a polygon. For example, the interior angles of a triangle always add up to 180°, and the interior angles of a quadrilateral always add up to 360°.

Overall, supplementary angles are an important concept in both real world scenarios and mathematical problems. By understanding how to use supplementary angles, engineers, pilots, sailors, and mathematicians can solve problems and make accurate calculations.

 

Adjacent Supplementary Angles

Adjacent supplementary angles are two angles that share a common vertex and a common side, and their non-shared sides form a straight angle. In other words, they are adjacent angles that add up to 180 degrees.

Adjacent Angles

Adjacent supplementary angles are the most common type of supplementary angles. They are formed when two angles share a common vertex and a common side, and their non-shared sides form a straight angle. For example, in the figure below, angles AOB and BOC are adjacent supplementary angles.

Non-Adjacent Angles

Non-adjacent supplementary angles are two angles that do not share a common vertex or a common side, but their measures add up to 180 degrees. They are also known as linear pair angles. For example, in the figure below, angles AOC and BOD are non-adjacent supplementary angles.

It is important to note that adjacent supplementary angles are always congruent, meaning that they have the same measure. Therefore, if you know the measure of one of the adjacent supplementary angles, you automatically know the measure of the other. On the other hand, non-adjacent supplementary angles are not necessarily congruent.

In summary, adjacent supplementary angles are two angles that share a common vertex and a common side, and their non-shared sides form a straight angle. Non-adjacent supplementary angles are two angles that do not share a common vertex or a common side, but their measures add up to 180 degrees.

 

FAQ about Supplementary Angles

What is the definition of supplementary angles?

Supplementary angles are two angles whose sum is equal to 180 degrees. In other words, when two angles are placed side by side, they form a straight line. These angles are called supplementary angles because they supplement each other to form a straight line.

Can two obtuse angles be supplementary?

Yes, two obtuse angles can be supplementary. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. When two obtuse angles are added together, they can equal 180 degrees, making them supplementary angles.

What is the sum of two supplementary angles?

The sum of two supplementary angles is always equal to 180 degrees. This is because supplementary angles, by definition, are two angles that add up to form a straight line.

What is an example of a pair of nonadjacent supplementary angles?

An example of a pair of nonadjacent supplementary angles is when two angles are separated by another angle. For example, if angle A measures 120 degrees, and angle B measures 60 degrees, then angle C must measure 180 – 120 – 60 = 0 degrees. Angles A and B are nonadjacent supplementary angles because they add up to 180 degrees, but they are separated by angle C.

What is the difference between complementary and supplementary angles?

Complementary angles are two angles whose sum is equal to 90 degrees, while supplementary angles are two angles whose sum is equal to 180 degrees. In other words, complementary angles add up to a right angle, while supplementary angles add up to a straight line.

How do you identify supplementary angles?

To identify supplementary angles, you need to add the two angles together. If the sum of the two angles is equal to 180 degrees, then the angles are supplementary.

Can three angles be supplementary?

No, three angles cannot be supplementary. Supplementary angles are always a pair of two angles that add up to 180 degrees. Therefore, it is impossible for three angles to be supplementary.

What angles cannot be supplementary?

Angles that cannot be supplementary are any two angles whose sum is not equal to 180 degrees. For example, two angles that add up to 90 degrees cannot be supplementary because they do not form a straight line.

 

Supplementary Angles worksheet Video Explanation

Watch our free video on do Supplementary Angles add up to 180. This video shows how to solve problems that are on our free Supplementary Angles worksheets that you can get by submitting your email above.

Watch the free Supplementary Angles video on YouTube here: Supplementary Angles Video

Video Transcript:

This video is about answering the question what are supplementary angles. You can get this finding supplementary angle worksheet for free by clicking on the link in the description below.

The first thing we need to talk about is what are supplementary angles and what is the definition of supplementary angles? The supplementary angles definition is when you have two angles that are added together to get 180 degrees. 180 degrees is just a straight line. IN this example at the bottom, we have a straight line. You can see that there is a ray coming off of the straight like to create two angles. If you look, we already know that this angle here is 50 degree, but we don’t know how many degrees the second angle is. We do know that supplementary angles are 180 degree. We know that one angle is 50 degrees so we know that we can do 180 degrees minus 50 degrees to get the missing angle. This missing angle has to be 130 degrees because the two angles together have to add up to 180 degrees. So if one supplementary angle is 50 degrees then the second supplementary angle has to be 130 degrees because the two added together have to add up to 180 degrees.

Let’s do a couple practice problems on our supplementary angles worksheet. We already know that the supplementary angle definition is that when one angle plus a second angle add up to 180 degrees. We already know that a straight line is equal to 180 degrees. In the case of number one, we know the first angle is 135 and we know that both angles have to add up to 180 degrees because they form a straight line. We know that both angles together have to add up to 180 degree. So we are going to take 180 degrees and subtract it from the angle that we know which is 135 degrees. When you subtract 180 minus 135 you get 45 degrees as the difference. Which means that this missing angle has to be 45 degrees because the two added together have to add up to 180 because they are supplementary.

Jumping down to number two on our supplementary angles examples. Again, the definition of supplementary angles is that when one angle plus a second angle adds up to 180 degrees. We know that this angle here is 128 and we know that this line had to equal 180 degrees total. So we know that the missing angle has to be the difference between 180 degrees and 128 degrees. You do 180 degrees subtracted by 128 degrees to get the difference of 52 degrees. Now we know that this angle has to be 52 degrees.

The last question that were going to do on our supplementary angles examples is number 5. Again, we know that supplementary angles definition is that when two angles add up to 180 degrees. This problem gives us one angle that is 45 degrees and an ingle that we don’t know. But we do know that a straight line adds up to 180 degrees. To get the missing angle were going to do 180 degrees minus the angle that we do know, which is 45 degrees. We get the answer of 135 degrees. So, the missing angle is 135 degrees.

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