Two Angles A And B Are Complementary. The Measure Of A Is 67. Write And Solve And Equation To Determine The Measure Of B. Check Your Solution

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Introduction

In geometry, complementary angles are two angles whose measures add up to 90 degrees. In this article, we will explore the concept of complementary angles and use an equation to find the measure of angle B, given that angle A is 67 degrees.

What are Complementary Angles?

Complementary angles are two angles whose measures add up to 90 degrees. This means that if we have two angles, A and B, and they are complementary, then:

A + B = 90

Given Information

We are given that angle A is 67 degrees. We need to find the measure of angle B.

Equation to Find Angle B

Since angles A and B are complementary, we can write the equation:

A + B = 90

Substituting the value of angle A, we get:

67 + B = 90

Solving for Angle B

To find the measure of angle B, we need to isolate B on one side of the equation. We can do this by subtracting 67 from both sides of the equation:

B = 90 - 67

B = 23

Checking the Solution

To check our solution, we can substitute the value of angle B back into the original equation:

A + B = 90

67 + 23 = 90

90 = 90

Since the equation holds true, our solution is correct.

Conclusion

In this article, we used an equation to find the measure of angle B, given that angle A is 67 degrees. We found that angle B is 23 degrees. We also checked our solution by substituting the value of angle B back into the original equation.

Real-World Applications

Complementary angles have many real-world applications, such as:

  • Architecture: Complementary angles are used in the design of buildings and bridges to create aesthetically pleasing and functional structures.
  • Engineering: Complementary angles are used in the design of mechanical systems, such as gears and pulleys, to create efficient and reliable systems.
  • Art: Complementary angles are used in the creation of art pieces, such as paintings and sculptures, to create visually appealing and thought-provoking works.

Tips and Tricks

Here are some tips and tricks to help you work with complementary angles:

  • Use a protractor: A protractor is a tool that can help you measure angles accurately.
  • Draw a diagram: Drawing a diagram can help you visualize the problem and find the solution.
  • Check your work: Always check your work by substituting the value of the unknown angle back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when working with complementary angles:

  • Not checking your work: Failing to check your work can lead to incorrect solutions.
  • Not using a protractor: Not using a protractor can lead to inaccurate measurements.
  • Not drawing a diagram: Not drawing a diagram can make it difficult to visualize the problem and find the solution.

Practice Problems

Here are some practice problems to help you practice working with complementary angles:

  • Problem 1: Find the measure of angle B, given that angle A is 45 degrees.
  • Problem 2: Find the measure of angle B, given that angle A is 30 degrees.
  • Problem 3: Find the measure of angle B, given that angle A is 60 degrees.

Answer Key

Here are the answers to the practice problems:

  • Problem 1: Angle B is 45 degrees.
  • Problem 2: Angle B is 60 degrees.
  • Problem 3: Angle B is 30 degrees.

Conclusion

Introduction

In our previous article, we explored the concept of complementary angles and used an equation to find the measure of angle B, given that angle A is 67 degrees. In this article, we will answer some frequently asked questions about complementary angles.

Q: What are complementary angles?

A: Complementary angles are two angles whose measures add up to 90 degrees.

Q: How do I find the measure of an angle if I know the measure of its complementary angle?

A: To find the measure of an angle if you know the measure of its complementary angle, you can use the equation:

A + B = 90

where A is the measure of the angle you know, and B is the measure of the angle you want to find.

Q: What is the difference between complementary angles and supplementary angles?

A: Complementary angles are two angles whose measures add up to 90 degrees, while supplementary angles are two angles whose measures add up to 180 degrees.

Q: Can I use the same equation to find the measure of an angle if I know the measure of its supplementary angle?

A: No, you cannot use the same equation to find the measure of an angle if you know the measure of its supplementary angle. To find the measure of an angle if you know the measure of its supplementary angle, you can use the equation:

A + B = 180

Q: How do I know if two angles are complementary or supplementary?

A: To determine if two angles are complementary or supplementary, you can add their measures together. If the sum is 90 degrees, the angles are complementary. If the sum is 180 degrees, the angles are supplementary.

Q: Can I have more than two complementary angles?

A: No, by definition, complementary angles are two angles whose measures add up to 90 degrees. You cannot have more than two complementary angles.

Q: Can I have more than two supplementary angles?

A: Yes, you can have more than two supplementary angles. For example, if you have three angles whose measures add up to 180 degrees, they are supplementary.

Q: How do I use complementary angles in real-world applications?

A: Complementary angles have many real-world applications, such as:

  • Architecture: Complementary angles are used in the design of buildings and bridges to create aesthetically pleasing and functional structures.
  • Engineering: Complementary angles are used in the design of mechanical systems, such as gears and pulleys, to create efficient and reliable systems.
  • Art: Complementary angles are used in the creation of art pieces, such as paintings and sculptures, to create visually appealing and thought-provoking works.

Q: What are some common mistakes to avoid when working with complementary angles?

A: Some common mistakes to avoid when working with complementary angles include:

  • Not checking your work: Failing to check your work can lead to incorrect solutions.
  • Not using a protractor: Not using a protractor can lead to inaccurate measurements.
  • Not drawing a diagram: Not drawing a diagram can make it difficult to visualize the problem and find the solution.

Q: How do I practice working with complementary angles?

A: You can practice working with complementary angles by:

  • Solving problems: Try solving problems that involve complementary angles.
  • Drawing diagrams: Draw diagrams to visualize the problem and find the solution.
  • Using a protractor: Use a protractor to measure angles accurately.

Conclusion

In this article, we answered some frequently asked questions about complementary angles. We hope this article has helped you understand the concept of complementary angles and how to use equations to find the measure of an angle.