1. **State the problem:** We are given an angle that is 60 degrees less than two times its supplement. We need to find the greater angle. 2. **Define variables:** Let the angle be $x$ degrees. 3. **Recall the supplement rule:** Two angles are supplementary if their sum is 180 degrees. So, the supplement of $x$ is $180 - x$. 4. **Set up the equation:** The angle $x$ is 60 degrees less than two times its supplement, so: $$x = 2(180 - x) - 60$$ 5. **Simplify the equation:** $$x = 360 - 2x - 60$$ $$x = 300 - 2x$$ 6. **Add $2x$ to both sides:** $$x + 2x = 300$$ $$3x = 300$$ 7. **Divide both sides by 3:** $$\cancel{3}x = \frac{300}{\cancel{3}}$$ $$x = 100$$ 8. **Find the supplement:** $$180 - x = 180 - 100 = 80$$ 9. **Identify the greater angle:** Between $x = 100$ and its supplement $80$, the greater angle is $100$ degrees. **Final answer:** The greater angle is $100$ degrees.