Answer :
To solve this problem, let's start with the properties of supplementary angles. When two angles are supplementary, the sum of their measures is [tex]\(180^\circ\)[/tex].
We are given that angle [tex]\(X\)[/tex] is 3 times the measure of angle [tex]\(Y\)[/tex]. Let's denote the measure of angle [tex]\(Y\)[/tex] by [tex]\(y\)[/tex]. Thus, the measure of angle [tex]\(X\)[/tex] can be represented as [tex]\(3y\)[/tex].
Given that [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] are supplementary:
[tex]\[ X + Y = 180^\circ \][/tex]
Substitute [tex]\(X = 3y\)[/tex]:
[tex]\[ 3y + y = 180^\circ \][/tex]
Combine like terms:
[tex]\[ 4y = 180^\circ \][/tex]
Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{180^\circ}{4} \][/tex]
[tex]\[ y = 45^\circ \][/tex]
Now that we have the measure of angle [tex]\(Y\)[/tex], we can find the measure of angle [tex]\(X\)[/tex]:
[tex]\[ X = 3y \][/tex]
[tex]\[ X = 3 \times 45^\circ \][/tex]
[tex]\[ X = 135^\circ \][/tex]
Thus, the measure of angle [tex]\(X\)[/tex] is [tex]\(135^\circ\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
We are given that angle [tex]\(X\)[/tex] is 3 times the measure of angle [tex]\(Y\)[/tex]. Let's denote the measure of angle [tex]\(Y\)[/tex] by [tex]\(y\)[/tex]. Thus, the measure of angle [tex]\(X\)[/tex] can be represented as [tex]\(3y\)[/tex].
Given that [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] are supplementary:
[tex]\[ X + Y = 180^\circ \][/tex]
Substitute [tex]\(X = 3y\)[/tex]:
[tex]\[ 3y + y = 180^\circ \][/tex]
Combine like terms:
[tex]\[ 4y = 180^\circ \][/tex]
Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{180^\circ}{4} \][/tex]
[tex]\[ y = 45^\circ \][/tex]
Now that we have the measure of angle [tex]\(Y\)[/tex], we can find the measure of angle [tex]\(X\)[/tex]:
[tex]\[ X = 3y \][/tex]
[tex]\[ X = 3 \times 45^\circ \][/tex]
[tex]\[ X = 135^\circ \][/tex]
Thus, the measure of angle [tex]\(X\)[/tex] is [tex]\(135^\circ\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
