Angles [tex]$X[tex]$[/tex] and [tex]$[/tex]Y[tex]$[/tex] are supplementary. Angle [tex]$[/tex]X[tex]$[/tex] is 3 times the measure of angle [tex]$[/tex]Y[tex]$[/tex]. What is the measure of angle [tex]$[/tex]X$[/tex]?

A. [tex]45^{\circ}[/tex]
B. [tex]60^{\circ}[/tex]
C. [tex]120^{\circ}[/tex]
D. [tex]135^{\circ}[/tex]



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]