Certainly! Let's solve this step-by-step.
1. Understand what supplementary angles are:
Supplementary angles are two angles whose measures add up to 180 degrees.
2. Given ratio:
The ratio of the measures of the two supplementary angles is given as 11:7.
3. Express the angles in terms of a variable:
Let's denote the measures of the angles as [tex]\(11x\)[/tex] and [tex]\(7x\)[/tex], where [tex]\(x\)[/tex] is a proportionality constant.
4. Set up the equation:
Since the angles are supplementary, their sum must be 180 degrees. Therefore,
[tex]\[
11x + 7x = 180
\][/tex]
5. Combine like terms:
[tex]\[
18x = 180
\][/tex]
6. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 18:
[tex]\[
x = \frac{180}{18}
\][/tex]
[tex]\[
x = 10
\][/tex]
7. Determine the measures of the angles:
- The first angle is:
[tex]\[
11x = 11 \times 10 = 110 \text{ degrees}
\][/tex]
- The second angle is:
[tex]\[
7x = 7 \times 10 = 70 \text{ degrees}
\][/tex]
8. Conclusion:
The measures of the angles are [tex]\(110\)[/tex] degrees and [tex]\(70\)[/tex] degrees.
