1. **State the problem:** We have a triangle with two known angles 57° and 60°, and two unknown angles $x$ and $y$ adjacent to the triangle on a straight horizontal line. We need to find $x$ and $y$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is always 180°. So, $$57^\circ + 60^\circ + \text{third angle} = 180^\circ$$ 3. **Calculate the third angle of the triangle:** $$\text{third angle} = 180^\circ - 57^\circ - 60^\circ = 63^\circ$$ 4. **Understand the straight line angle rule:** Angles on a straight line sum to 180°. Since $x$ and $y$ are adjacent to the triangle angles on the same horizontal line, each forms a linear pair with one of the triangle's angles. 5. **Find $x$:** $x$ is adjacent to the 57° angle, so $$x + 57^\circ = 180^\circ$$ $$x = 180^\circ - 57^\circ = 123^\circ$$ 6. **Find $y$:** $y$ is adjacent to the 60° angle, so $$y + 60^\circ = 180^\circ$$ $$y = 180^\circ - 60^\circ = 120^\circ$$ **Final answers:** $$x = 123^\circ, \quad y = 120^\circ$$