Supplementary Angles Cabaeb

1. **State the problem:** We need to find two supplementary angles whose difference is 42 degrees. 2. **Recall the definition:** Supplementary angles add up to 180 degrees. So if the two angles are $x$ and $y$, then: $$x + y = 180$$ 3. **Given condition:** The difference between the two angles is 42 degrees: $$x - y = 42$$ 4. **Solve the system of equations:** Add the two equations: $$\begin{aligned} (x + y) + (x - y) &= 180 + 42 \\ 2x &= 222 \\ x &= \frac{222}{2} = 111 \end{aligned}$$ 5. **Find $y$:** Substitute $x = 111$ into $x + y = 180$: $$111 + y = 180$$ $$y = 180 - 111 = 69$$ 6. **Answer:** The two supplementary angles are $111$ degrees and $69$ degrees.