Answer :
To solve the problem where angles \( X \) and \( Y \) are supplementary, and angle \( X \) is 3 times the measure of angle \( Y \), we can follow these steps:
1. Understand the properties of supplementary angles:
Supplementary angles are two angles whose measures add up to 180 degrees. Therefore, we have the equation:
[tex]\[ X + Y = 180^\circ \][/tex]
2. Express angle \( X \) in terms of angle \( Y \):
Given that angle \( X \) is 3 times the measure of angle \( Y \), we can write:
[tex]\[ X = 3Y \][/tex]
3. Substitute the expression for \( X \) into the supplementary angle equation:
Substitute \( X = 3Y \) into the equation \( X + Y = 180^\circ \):
[tex]\[ 3Y + Y = 180^\circ \][/tex]
Simplify the equation:
[tex]\[ 4Y = 180^\circ \][/tex]
4. Solve for angle \( Y \):
Divide both sides of the equation by 4:
[tex]\[ Y = \frac{180^\circ}{4} = 45^\circ \][/tex]
5. Determine the measure of angle \( X \):
Since \( X \) is 3 times the measure of \( Y \), we have:
[tex]\[ X = 3Y = 3 \times 45^\circ = 135^\circ \][/tex]
Therefore, the measure of angle \( X \) is:
[tex]\[ 135^\circ \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
1. Understand the properties of supplementary angles:
Supplementary angles are two angles whose measures add up to 180 degrees. Therefore, we have the equation:
[tex]\[ X + Y = 180^\circ \][/tex]
2. Express angle \( X \) in terms of angle \( Y \):
Given that angle \( X \) is 3 times the measure of angle \( Y \), we can write:
[tex]\[ X = 3Y \][/tex]
3. Substitute the expression for \( X \) into the supplementary angle equation:
Substitute \( X = 3Y \) into the equation \( X + Y = 180^\circ \):
[tex]\[ 3Y + Y = 180^\circ \][/tex]
Simplify the equation:
[tex]\[ 4Y = 180^\circ \][/tex]
4. Solve for angle \( Y \):
Divide both sides of the equation by 4:
[tex]\[ Y = \frac{180^\circ}{4} = 45^\circ \][/tex]
5. Determine the measure of angle \( X \):
Since \( X \) is 3 times the measure of \( Y \), we have:
[tex]\[ X = 3Y = 3 \times 45^\circ = 135^\circ \][/tex]
Therefore, the measure of angle \( X \) is:
[tex]\[ 135^\circ \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
