To solve this problem, follow these step-by-step instructions:
1. Understand the concept of supplementary angles:
Supplementary angles are two angles whose measures add up to [tex]\(180^{\circ}\)[/tex].
2. Set up the relationship between the angles:
Let the measure of the smaller angle be [tex]\(x\)[/tex] degrees. According to the problem, the measure of the greater angle is [tex]\(44^{\circ}\)[/tex] more than the measure of the smaller angle. Therefore, the measure of the greater angle is [tex]\(x + 44^{\circ}\)[/tex].
3. Write the equation based on the supplementary angles:
Since the two angles are supplementary, their measures add up to [tex]\(180^{\circ}\)[/tex]. This gives us the equation:
[tex]\[
x + (x + 44) = 180
\][/tex]
4. Simplify and solve the equation:
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
x + x + 44 = 180
\][/tex]
[tex]\[
2x + 44 = 180
\][/tex]
5. Isolate [tex]\(x\)[/tex]:
Subtract 44 from both sides of the equation:
[tex]\[
2x = 180 - 44
\][/tex]
[tex]\[
2x = 136
\][/tex]
6. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2:
[tex]\[
x = \frac{136}{2}
\][/tex]
[tex]\[
x = 68
\][/tex]
7. Determine the measures of the angles:
- The measure of the smaller angle is [tex]\(x\)[/tex], which is [tex]\(68^{\circ}\)[/tex].
- The measure of the greater angle is [tex]\(x + 44\)[/tex], which is [tex]\(68 + 44 = 112^{\circ}\)[/tex].
Hence, the measures of the two supplementary angles are:
- Smaller angle: [tex]\(68^{\circ}\)[/tex]
- Greater angle: [tex]\(112^{\circ}\)[/tex]
