1. **State the problem:** We need to find an angle whose complement measures 20 degrees less than one-third of its supplement. 2. **Recall definitions:** - The complement of an angle $x$ is $90 - x$ degrees. - The supplement of an angle $x$ is $180 - x$ degrees. 3. **Set up the equation:** According to the problem, $$90 - x = \frac{1}{3}(180 - x) - 20$$ 4. **Solve the equation:** Multiply both sides by 3 to clear the fraction: $$3(90 - x) = 180 - x - 60$$ $$270 - 3x = 120 - x$$ Add $3x$ to both sides and subtract $120$ from both sides: $$270 - 120 = -x + 3x$$ $$150 = 2x$$ Divide both sides by 2: $$x = \frac{150}{2} = 75$$ 5. **Interpret the result:** The angle measures $75$ degrees. 6. **Check:** - Complement: $90 - 75 = 15$ - Supplement: $180 - 75 = 105$ - One-third of supplement minus 20: $\frac{1}{3} \times 105 - 20 = 35 - 20 = 15$ The complement equals 15, which matches the right side, confirming the solution. **Final answer:** The angle measures $75$ degrees.