Answer :
Certainly! Let's solve this problem step-by-step.
1. Understanding Supplementary Angles:
Supplementary angles are two angles whose measures add up to 180 degrees.
2. Define the Angles:
- Let the measure of angle Y be denoted by [tex]\( y \)[/tex].
- According to the problem, angle X is 3 times the measure of angle Y. So, we can write the measure of angle X as [tex]\( 3y \)[/tex].
3. Set Up the Equation:
Since angles X and Y are supplementary, their sum is 180 degrees. We can write the equation:
[tex]\[ X + Y = 180^\circ \][/tex]
Substituting [tex]\( X = 3y \)[/tex], the equation becomes:
[tex]\[ 3y + y = 180^\circ \][/tex]
4. Solve for [tex]\( y \)[/tex]:
Combine the terms on the left side of the equation:
[tex]\[ 4y = 180^\circ \][/tex]
Divide both sides by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{180}{4} = 45^\circ \][/tex]
5. Find the Measure of Angle X:
Now that we have the measure of angle Y, we can find the measure of angle X:
[tex]\[ X = 3y = 3 \times 45^\circ = 135^\circ \][/tex]
Therefore, the measure of angle X is [tex]\( 135^\circ \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
1. Understanding Supplementary Angles:
Supplementary angles are two angles whose measures add up to 180 degrees.
2. Define the Angles:
- Let the measure of angle Y be denoted by [tex]\( y \)[/tex].
- According to the problem, angle X is 3 times the measure of angle Y. So, we can write the measure of angle X as [tex]\( 3y \)[/tex].
3. Set Up the Equation:
Since angles X and Y are supplementary, their sum is 180 degrees. We can write the equation:
[tex]\[ X + Y = 180^\circ \][/tex]
Substituting [tex]\( X = 3y \)[/tex], the equation becomes:
[tex]\[ 3y + y = 180^\circ \][/tex]
4. Solve for [tex]\( y \)[/tex]:
Combine the terms on the left side of the equation:
[tex]\[ 4y = 180^\circ \][/tex]
Divide both sides by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{180}{4} = 45^\circ \][/tex]
5. Find the Measure of Angle X:
Now that we have the measure of angle Y, we can find the measure of angle X:
[tex]\[ X = 3y = 3 \times 45^\circ = 135^\circ \][/tex]
Therefore, the measure of angle X is [tex]\( 135^\circ \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{135^\circ} \][/tex]
