Finding the Measure of the Angle

Oct 13, 2025 by windailys.com 69 views

Introduction

In geometry, angles are a fundamental concept that plays a crucial role in various mathematical operations. Angles can be classified into different types, such as acute, right, obtuse, and straight angles. In this article, we will focus on the concept of supplementary angles and how to find the measure of an angle when its supplementary angle is known.

What are Supplementary Angles?

Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if we have two angles, say ∠A and ∠B, and their sum is 180 degrees, then they are supplementary angles. Mathematically, this can be represented as:

∠A + ∠B = 180°

The Problem

The problem states that the measure of an angle is twice the measure of its supplementary angle. Let's assume that the measure of the supplementary angle is x degrees. Then, the measure of the angle in question is 2x degrees. Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°

Solving the Equation

To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°

Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°

Finding the Measure of the Angle

Now that we have found the measure of the supplementary angle, we can find the measure of the angle in question. Since the measure of the angle is twice the measure of its supplementary angle, we can multiply the measure of the supplementary angle by 2:

Measure of the angle = 2x = 2(60°) = 120°

Conclusion

In this article, we discussed the concept of supplementary angles and how to find the measure of an angle when its supplementary angle is known. We used a simple equation to solve for the measure of the supplementary angle and then found the measure of the angle in question. The final answer is 120 degrees.

Example Problems

If the measure of a supplementary angle is 40 degrees, what is the measure of the other angle?
If the measure of a supplementary angle is 80 degrees, what is the measure of the other angle?

Step-by-Step Solution

To solve these problems, we can follow the same steps as before:

Let's assume that the measure of the supplementary angle is x degrees.
The measure of the other angle is 2x degrees.
Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°
To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°
Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°
Now that we have found the measure of the supplementary angle, we can find the measure of the other angle. Since the measure of the other angle is twice the measure of its supplementary angle, we can multiply the measure of the supplementary angle by 2:

Measure of the other angle = 2x = 2(60°) = 120°

Real-World Applications

The concept of supplementary angles has numerous real-world applications. For example:

In architecture, supplementary angles are used to design buildings and structures. Architects use angles to create symmetrical and aesthetically pleasing designs.
In engineering, supplementary angles are used to design machines and mechanisms. Engineers use angles to create efficient and effective systems.
In navigation, supplementary angles are used to determine directions and locations. Pilots and sailors use angles to navigate through unfamiliar territories.

Conclusion

In conclusion, the concept of supplementary angles is a fundamental concept in geometry that has numerous real-world applications. By understanding how to find the measure of an angle when its supplementary angle is known, we can solve a wide range of problems in various fields. The final answer is 120 degrees.

Frequently Asked Questions

What is the measure of an angle when its supplementary angle is 40 degrees?
What is the measure of an angle when its supplementary angle is 80 degrees?

Step-by-Step Solution

To solve these problems, we can follow the same steps as before:

Let's assume that the measure of the supplementary angle is x degrees.
The measure of the other angle is 2x degrees.
Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°
To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°
Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°
Now that we have found the measure of the supplementary angle, we can find the measure of the other angle. Since the measure of the other angle is twice the measure of its supplementary angle, we can multiply the measure of the supplementary angle by 2:

Measure of the other angle = 2x = 2(60°) = 120°

Final Answer

The final answer is 120 degrees.

Introduction

In our previous article, we discussed the concept of supplementary angles and how to find the measure of an angle when its supplementary angle is known. In this article, we will address some of the most frequently asked questions (FAQs) related to supplementary angles.

Q1: What is the measure of an angle when its supplementary angle is 40 degrees?

A1:

To find the measure of the angle, we need to use the formula:

Measure of the angle = 2x

where x is the measure of the supplementary angle.

First, we need to find the measure of the supplementary angle. Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°

To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°

Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°

Now that we have found the measure of the supplementary angle, we can find the measure of the angle. Since the measure of the angle is twice the measure of its supplementary angle, we can multiply the measure of the supplementary angle by 2:

Measure of the angle = 2x = 2(60°) = 120°

Q2: What is the measure of an angle when its supplementary angle is 80 degrees?

A2:

To find the measure of the angle, we need to use the formula:

Measure of the angle = 2x

where x is the measure of the supplementary angle.

First, we need to find the measure of the supplementary angle. Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°

To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°

Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°

Measure of the angle = 2x = 2(60°) = 120°

Q3: What is the difference between supplementary and complementary angles?

A3:

Supplementary angles are two angles whose measures add up to 180 degrees. Complementary angles, on the other hand, are two angles whose measures add up to 90 degrees.

Q4: How do I find the measure of an angle when its complementary angle is known?

A4:

To find the measure of an angle when its complementary angle is known, we can use the formula:

Measure of the angle = 90° - x

where x is the measure of the complementary angle.

Q5: What is the measure of an angle when its complementary angle is 30 degrees?

A5:

To find the measure of the angle, we need to use the formula:

Measure of the angle = 90° - x

where x is the measure of the complementary angle.

First, we need to find the measure of the angle. Since the two angles are complementary, their sum is 90 degrees. We can set up an equation to represent this relationship:

x + (90° - x) = 90°

To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

90° = 90°

This equation is true for all values of x, so we can conclude that the measure of the angle is:

Measure of the angle = 90° - x = 90° - 30° = 60°

Q6: What is the measure of an angle when its supplementary angle is 50 degrees?

A6:

To find the measure of the angle, we need to use the formula:

Measure of the angle = 2x

where x is the measure of the supplementary angle.

First, we need to find the measure of the supplementary angle. Since the two angles are supplementary, their sum is 180 degrees. We can set up an equation to represent this relationship:

x + 2x = 180°

To solve the equation, we need to combine like terms. In this case, we have two x terms, so we can add them together:

3x = 180°

Next, we need to isolate the variable x by dividing both sides of the equation by 3:

x = 180° / 3

x = 60°

Measure of the angle = 2x = 2(60°) = 120°

Conclusion

In this article, we addressed some of the most frequently asked questions (FAQs) related to supplementary angles. We provided step-by-step solutions to each question and explained the concepts in detail. We hope that this article has been helpful in clarifying any doubts you may have had about supplementary angles.