B)-14,6 9, -1 D) -9,1 ii) If Two Supplementary Angles Are In The Ratio 1: 3, Then The Bigger Angle Is a) 135° B) 60° C) 120 D) 180

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Introduction

In mathematics, supplementary angles are two angles whose sum is equal to 180 degrees. These angles are essential in various mathematical concepts, including trigonometry and geometry. In this article, we will explore the concept of supplementary angles and their ratios, focusing on the given problem of two supplementary angles in the ratio 1:3.

What are Supplementary Angles?

Supplementary angles are two angles whose sum is equal to 180 degrees. For example, if we have two angles, ∠A and ∠B, and their sum is 180 degrees, then they are supplementary angles. This can be represented mathematically as:

∠A + ∠B = 180°

Understanding Angle Ratios

Angle ratios are used to compare the sizes of two or more angles. In the given problem, we are dealing with two supplementary angles in the ratio 1:3. This means that the smaller angle is 1 part, and the larger angle is 3 parts. We can represent this ratio as:

∠A : ∠B = 1 : 3

Solving the Problem

To solve the problem, we need to find the value of the larger angle. Since the two angles are supplementary, their sum is equal to 180 degrees. We can use this information to set up an equation and solve for the larger angle.

Let's assume that the smaller angle is x degrees. Then, the larger angle is 3x degrees. Since the sum of the two angles is 180 degrees, we can set up the following equation:

x + 3x = 180

Combine like terms:

4x = 180

Divide both sides by 4:

x = 45

Now that we have found the value of the smaller angle, we can find the value of the larger angle by multiplying x by 3:

3x = 3(45) = 135

Therefore, the larger angle is 135 degrees.

Conclusion

In conclusion, we have explored the concept of supplementary angles and their ratios. We have used the given problem to find the value of the larger angle, which is 135 degrees. This problem demonstrates the importance of understanding angle ratios and how they can be used to solve mathematical problems.

Answer to the Problem

The answer to the problem is:

a) 135°

Additional Examples

Here are a few additional examples of supplementary angles and their ratios:

  • If two supplementary angles are in the ratio 2:5, then the larger angle is: a) 120° b) 150° c) 180° d) 210° Answer: a) 120°
  • If two supplementary angles are in the ratio 3:4, then the larger angle is: a) 90° b) 120° c) 135° d) 150° Answer: c) 135°

Final Thoughts

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about supplementary angles and their ratios.

Q: What are supplementary angles?

A: Supplementary angles are two angles whose sum is equal to 180 degrees.

Q: How do I find the value of a supplementary angle?

A: To find the value of a supplementary angle, you need to know the value of the other angle. If you know the value of one angle, you can use the fact that the sum of the two angles is 180 degrees to find the value of the other angle.

Q: What is the ratio of supplementary angles?

A: The ratio of supplementary angles is the comparison of the sizes of the two angles. For example, if two supplementary angles are in the ratio 1:3, the smaller angle is 1 part, and the larger angle is 3 parts.

Q: How do I find the value of the larger angle in a supplementary angle ratio?

A: To find the value of the larger angle in a supplementary angle ratio, you need to know the value of the smaller angle. If you know the value of the smaller angle, you can multiply it by the ratio to find the value of the larger angle.

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

A: Supplementary angles are two angles whose sum is equal to 180 degrees, while complementary angles are two angles whose sum is equal to 90 degrees.

Q: Can supplementary angles be negative?

A: No, supplementary angles cannot be negative. Angles are measured in degrees, and the sum of two angles cannot be negative.

Q: Can supplementary angles be zero?

A: No, supplementary angles cannot be zero. If one angle is zero, the other angle must be 180 degrees to make the sum equal to 180 degrees.

Q: How do I use supplementary angles in real-life situations?

A: Supplementary angles are used in various real-life situations, such as:

  • Architecture: When designing buildings, architects use supplementary angles to ensure that the walls and roof are properly aligned.
  • Engineering: Engineers use supplementary angles to design and build machines and mechanisms.
  • Physics: Physicists use supplementary angles to describe the motion of objects and the behavior of light.

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

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

  • Assuming that the sum of two angles is equal to 180 degrees without checking the ratio.
  • Failing to consider the ratio of the two angles when finding the value of one angle.
  • Not checking the units of measurement when working with angles.

Conclusion

In conclusion, supplementary angles and their ratios are essential concepts in mathematics. By understanding these concepts, you can solve mathematical problems and make informed decisions in various fields. We hope that this article has provided valuable insights into the world of supplementary angles and their ratios.

Additional Resources

For more information on supplementary angles and their ratios, check out the following resources:

  • Khan Academy: Supplementary Angles
  • Mathway: Supplementary Angles
  • Wolfram Alpha: Supplementary Angles

Final Thoughts

In conclusion, supplementary angles and their ratios are fundamental concepts in mathematics. By understanding these concepts, you can solve mathematical problems and make informed decisions in various fields. We hope that this article has provided valuable insights into the world of supplementary angles and their ratios.