It Is Given That X And Y Are Supplementary Angles. If X Is Greater Than Y By 54°, Find X And Y.
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Introduction
In this article, we will explore the concept of supplementary angles and how to find the values of two supplementary angles when one angle is greater than the other by a certain degree. We will use mathematical equations to solve for the values of x and y.
What are Supplementary Angles?
Supplementary angles are two angles whose sum is equal to 180°. In other words, if we have two angles, x and y, and they are supplementary, then x + y = 180°.
Given Information
It is given that x and y are supplementary angles. Additionally, it is given that x is greater than y by 54°. This can be expressed as:
x = y + 54°
Mathematical Equation
We can use the fact that x and y are supplementary angles to write a mathematical equation. Since x + y = 180°, we can substitute x = y + 54° into this equation:
(y + 54°) + y = 180°
Simplifying the Equation
We can simplify the equation by combining like terms:
2y + 54° = 180°
Solving for y
To solve for y, we need to isolate y on one side of the equation. We can do this by subtracting 54° from both sides of the equation:
2y = 180° - 54° 2y = 126°
Dividing by 2
To solve for y, we need to divide both sides of the equation by 2:
y = 126° / 2 y = 63°
Finding x
Now that we have found the value of y, we can find the value of x by substituting y = 63° into the equation x = y + 54°:
x = 63° + 54° x = 117°
Conclusion
In this article, we have found the values of two supplementary angles, x and y, when one angle is greater than the other by 54°. We used mathematical equations to solve for the values of x and y, and we found that x = 117° and y = 63°.
Frequently Asked Questions
- What are supplementary angles? Supplementary angles are two angles whose sum is equal to 180°.
- How do we find the values of two supplementary angles when one angle is greater than the other by a certain degree? We can use mathematical equations to solve for the values of x and y.
- What is the value of x in this problem? x = 117°
- What is the value of y in this problem? y = 63°
Step-by-Step Solution
- Write a mathematical equation using the fact that x and y are supplementary angles: x + y = 180°
- Substitute x = y + 54° into the equation: (y + 54°) + y = 180°
- Simplify the equation by combining like terms: 2y + 54° = 180°
- Subtract 54° from both sides of the equation: 2y = 180° - 54°
- Divide both sides of the equation by 2: y = 126° / 2
- Find the value of x by substituting y = 63° into the equation x = y + 54°: x = 63° + 54°
- Simplify the equation to find the value of x: x = 117°
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Introduction
In our previous article, we explored the concept of supplementary angles and how to find the values of two supplementary angles when one angle is greater than the other by a certain degree. In this article, we will answer some frequently asked questions about supplementary angles.
Q&A
Q: What are supplementary angles?
A: Supplementary angles are two angles whose sum is equal to 180°.
Q: How do we find the values of two supplementary angles when one angle is greater than the other by a certain degree?
A: We can use mathematical equations to solve for the values of x and y. We can write a mathematical equation using the fact that x and y are supplementary angles: x + y = 180°. Then, we can substitute x = y + 54° into the equation and simplify it to find the values of x and y.
Q: What is the value of x in this problem?
A: In the problem we discussed earlier, the value of x is 117°.
Q: What is the value of y in this problem?
A: In the problem we discussed earlier, the value of y is 63°.
Q: Can we have two supplementary angles that are equal?
A: No, we cannot have two supplementary angles that are equal. By definition, supplementary angles are two angles whose sum is equal to 180°. If the two angles are equal, then their sum would be twice the value of one angle, which is not equal to 180°.
Q: Can we have two supplementary angles that are negative?
A: No, we cannot have two supplementary angles that are negative. Angles are measured in degrees, and degrees are a positive quantity. Therefore, it is not possible to have two supplementary angles that are negative.
Q: Can we have two supplementary angles that are zero?
A: No, we cannot have two supplementary angles that are zero. By definition, supplementary angles are two angles whose sum is equal to 180°. If both angles are zero, then their sum would be zero, which is not equal to 180°.
Q: Can we have two supplementary angles that are obtuse?
A: Yes, we can have two supplementary angles that are obtuse. For example, if one angle is 120° and the other angle is 60°, then they are supplementary angles and both are obtuse.
Q: Can we have two supplementary angles that are acute?
A: Yes, we can have two supplementary angles that are acute. For example, if one angle is 60° and the other angle is 120°, then they are supplementary angles and both are acute.
Conclusion
In this article, we have answered some frequently asked questions about supplementary angles. We have discussed the definition of supplementary angles, how to find the values of two supplementary angles when one angle is greater than the other by a certain degree, and some common misconceptions about supplementary angles.
Frequently Asked Questions (FAQs)
- What are supplementary angles? Supplementary angles are two angles whose sum is equal to 180°.
- How do we find the values of two supplementary angles when one angle is greater than the other by a certain degree? We can use mathematical equations to solve for the values of x and y.
- What is the value of x in this problem? x = 117°
- What is the value of y in this problem? y = 63°
- Can we have two supplementary angles that are equal? No, we cannot have two supplementary angles that are equal.
- Can we have two supplementary angles that are negative? No, we cannot have two supplementary angles that are negative.
- Can we have two supplementary angles that are zero? No, we cannot have two supplementary angles that are zero.
- Can we have two supplementary angles that are obtuse? Yes, we can have two supplementary angles that are obtuse.
- Can we have two supplementary angles that are acute? Yes, we can have two supplementary angles that are acute.
Step-by-Step Solution
- Write a mathematical equation using the fact that x and y are supplementary angles: x + y = 180°
- Substitute x = y + 54° into the equation: (y + 54°) + y = 180°
- Simplify the equation by combining like terms: 2y + 54° = 180°
- Subtract 54° from both sides of the equation: 2y = 180° - 54°
- Divide both sides of the equation by 2: y = 126° / 2
- Find the value of x by substituting y = 63° into the equation x = y + 54°: x = 63° + 54°
- Simplify the equation to find the value of x: x = 117°