Certainly! To solve this problem, let's go through the process step-by-step:
1. Understanding Complementary Angles:
- Complementary angles are two angles whose measures add up to 90 degrees.
2. Set up the Variables:
- Let's denote the measure of the smaller angle as [tex]\( x \)[/tex].
- According to the problem, the measure of the other angle is three times the measure of the smaller angle. Therefore, the measure of the other angle would be [tex]\( 3x \)[/tex].
3. Set up the Equation:
- Since the two angles are complementary, their measures add up to 90 degrees. So, we can write the equation:
[tex]\[
x + 3x = 90
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Combine the like terms on the left side of the equation:
[tex]\[
4x = 90
\][/tex]
- To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
x = \frac{90}{4} = 22.5
\][/tex]
5. Find the Measure of the Other Angle:
- We know that the other angle is three times the measure of the smaller angle:
[tex]\[
3x = 3 \times 22.5 = 67.5
\][/tex]
6. Conclusion:
- The measures of the two complementary angles are:
- The smaller angle: [tex]\( 22.5 \)[/tex] degrees
- The larger angle: [tex]\( 67.5 \)[/tex] degrees
Therefore, the measures of the two complementary angles are 22.5 degrees and 67.5 degrees.
