Finding the Measure of Angle X

Oct 13, 2025 by recoveryshake.com 73 views

Understanding Supplementary Angles

In geometry, supplementary angles are two angles whose measures add up to 180 degrees. This concept is crucial in solving problems involving angles, and it's essential to understand how to work with supplementary angles to find the measure of a given angle.

The Problem: Angle X and Angle Y

We are given that angles X and Y are supplementary, meaning their measures add up to 180 degrees. Additionally, we know that angle X is 3 times the measure of angle Y. Let's denote the measure of angle Y as "y". Since angle X is 3 times the measure of angle Y, we can express the measure of angle X as "3y".

Setting Up the Equation

Since angles X and Y are supplementary, their measures add up to 180 degrees. We can set up an equation to represent this relationship:

X + Y = 180

Substituting the expressions for angles X and Y, we get:

3y + y = 180

Combine like terms:

4y = 180

Solving for Angle Y

To find the measure of angle Y, we need to solve for y. Divide both sides of the equation by 4:

y = 180 / 4

y = 45

Finding the Measure of Angle X

Now that we know the measure of angle Y, we can find the measure of angle X. Since angle X is 3 times the measure of angle Y, we can multiply the measure of angle Y by 3:

X = 3y

X = 3(45)

X = 135

Conclusion

In this problem, we used the concept of supplementary angles to find the measure of angle X. We set up an equation based on the given information and solved for the measure of angle Y. Then, we used the measure of angle Y to find the measure of angle X. The final answer is that the measure of angle X is 135 degrees.

Key Takeaways

Supplementary angles are two angles whose measures add up to 180 degrees.
We can use the concept of supplementary angles to solve problems involving angles.
To find the measure of a given angle, we need to set up an equation based on the given information and solve for the unknown angle.

Practice Problems

Angles A and B are supplementary. Angle A is 2 times the measure of angle B. What is the measure of angle A?
Angles C and D are supplementary. Angle C is 5 times the measure of angle D. What is the measure of angle C?
Angles E and F are supplementary. Angle E is 4 times the measure of angle F. What is the measure of angle E?

Answer Key

180
150
180
Supplementary Angles Q&A ==========================

Frequently Asked Questions

Q: What are supplementary angles?

A: Supplementary angles are two angles whose measures add up to 180 degrees.

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

A: To determine if two angles are supplementary, add their measures together. If the sum is 180 degrees, then the angles are supplementary.

Q: Can two angles be both supplementary and complementary at the same time?

A: No, two angles cannot be both supplementary and complementary at the same time. 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: How do I find the measure of a supplementary angle?

A: To find the measure of a supplementary angle, you need to know the measure of the other angle. If you know the measure of one angle, you can set up an equation to find the measure of the other angle.

Q: What is the relationship between supplementary angles and the sum of their measures?

A: The sum of the measures of two supplementary angles is always 180 degrees.

Q: Can I have a negative measure for a supplementary angle?

A: No, the measure of an angle cannot be negative. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle?

A: To find the measure of an angle that is supplementary to a given angle, you need to know the measure of the given angle. If you know the measure of the given angle, you can set up an equation to find the measure of the supplementary angle.

Q: Can two angles be supplementary if they have different measures?

A: Yes, two angles can be supplementary even if they have different measures. For example, if one angle measures 120 degrees and the other angle measures 60 degrees, they are supplementary because their measures add up to 180 degrees.

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

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

Q: Can I have a fraction as the measure of a supplementary angle?

A: Yes, you can have a fraction as the measure of a supplementary angle. For example, if one angle measures 1/2 of 180 degrees, then the other angle must measure 1/2 of 180 degrees as well, because their measures add up to 180 degrees.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a fraction?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a fraction, you need to multiply the fraction by the total measure of the supplementary angles (180 degrees). For example, if the given angle is 1/2 of 180 degrees, then the supplementary angle must be 1/2 of 180 degrees as well.

Q: Can I have a decimal as the measure of a supplementary angle?

A: Yes, you can have a decimal as the measure of a supplementary angle. For example, if one angle measures 0.5 of 180 degrees, then the other angle must measure 0.5 of 180 degrees as well, because their measures add up to 180 degrees.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal, you need to multiply the decimal by the total measure of the supplementary angles (180 degrees). For example, if the given angle is 0.5 of 180 degrees, then the supplementary angle must be 0.5 of 180 degrees as well.

Q: Can I have a mixed number as the measure of a supplementary angle?

A: Yes, you can have a mixed number as the measure of a supplementary angle. For example, if one angle measures 2 1/2 of 180 degrees, then the other angle must measure 2 1/2 of 180 degrees as well, because their measures add up to 180 degrees.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a mixed number?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a mixed number, you need to multiply the mixed number by the total measure of the supplementary angles (180 degrees). For example, if the given angle is 2 1/2 of 180 degrees, then the supplementary angle must be 2 1/2 of 180 degrees as well.

Q: Can I have a negative mixed number as the measure of a supplementary angle?

A: No, the measure of an angle cannot be a negative mixed number. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a negative mixed number?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a negative mixed number, you need to convert the negative mixed number to a positive mixed number, and then multiply it by the total measure of the supplementary angles (180 degrees). For example, if the given angle is -2 1/2 of 180 degrees, then the supplementary angle must be 2 1/2 of 180 degrees, because their measures add up to 180 degrees.

Q: Can I have a decimal with a negative sign as the measure of a supplementary angle?

A: No, the measure of an angle cannot be a decimal with a negative sign. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal with a negative sign?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal with a negative sign, you need to convert the decimal with a negative sign to a positive decimal, and then multiply it by the total measure of the supplementary angles (180 degrees). For example, if the given angle is -0.5 of 180 degrees, then the supplementary angle must be 0.5 of 180 degrees, because their measures add up to 180 degrees.

Q: Can I have a fraction with a negative sign as the measure of a supplementary angle?

A: No, the measure of an angle cannot be a fraction with a negative sign. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a fraction with a negative sign?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a fraction with a negative sign, you need to convert the fraction with a negative sign to a positive fraction, and then multiply it by the total measure of the supplementary angles (180 degrees). For example, if the given angle is -1/2 of 180 degrees, then the supplementary angle must be 1/2 of 180 degrees, because their measures add up to 180 degrees.

Q: Can I have a mixed number with a negative sign as the measure of a supplementary angle?

A: No, the measure of an angle cannot be a mixed number with a negative sign. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a mixed number with a negative sign?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a mixed number with a negative sign, you need to convert the mixed number with a negative sign to a positive mixed number, and then multiply it by the total measure of the supplementary angles (180 degrees). For example, if the given angle is -2 1/2 of 180 degrees, then the supplementary angle must be 2 1/2 of 180 degrees, because their measures add up to 180 degrees.

Q: Can I have a decimal with a negative sign and a fraction as the measure of a supplementary angle?

A: No, the measure of an angle cannot be a decimal with a negative sign and a fraction. Angles are measured in degrees, and the measure of a supplementary angle must be a positive number.

Q: How do I find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal with a negative sign and a fraction?

A: To find the measure of an angle that is supplementary to a given angle, when the given angle is expressed as a decimal with a negative sign and a fraction, you need to convert the decimal with a negative sign and the fraction to a positive decimal, and then multiply it by the total measure of the supplementary angles (180 degrees). For example, if the given angle is -0.5 + 1/2 of 180 degrees, then the supplementary angle must be 0.5 + 1/2 of