Certainly! Let's solve the problem step-by-step.
Question: An angle measures 38° less than the measure of its supplementary angle. What is the measure of each angle?
Solution:
1. Understand the relationship between supplementary angles:
- Two angles are supplementary if the sum of their measures is 180°. In other words, if you have two angles \(\( \alpha \)\) and \(\( \beta \)\), then \(\( \alpha + \beta = 180° \)\).
2. Define the angles:
- Let the measure of the first angle be \(\( x \)\).
- The measure of its supplementary angle will then be \(\( 180° - x \)\).
3. Set up the equation based on the given information:
- We are told that the first angle is 38° less than its supplementary angle.
- Therefore, we can write the equation as:
\(\[
x = (180° - x) - 38°
\]\)
4. Solve the equation:
- Start by simplifying the right-hand side:
\(\[
x = 180° - x - 38°
\]\)
- Combine like terms:
\(\[
x + x = 180° - 38°
\]\)
- Simplify further:
\(\[
2x = 142°
\]\)
- Finally, solve for \(\( x \)\) by dividing both sides by 2:
\(\[
x = \frac{142°}{2}
\]\)
\(\[
x = 71°
\]\)
5. Find the measure of the supplementary angle:
- The supplementary angle is:
\(\[
180° - 71° = 109°
\]\)
Conclusion:
The measure of the first angle is \(\( 71° \)\) and the measure of the supplementary angle is \(\( 109° \)\).
So, the measures of the two angles are \(\( 71° \)\) and \(\( 109° \)\).
