1. **State the problem:** We have two connected triangles on a horizontal line. The left triangle has a top angle of 65°. The right triangle has a 40° angle at the left base, an unknown angle $x^\circ$ at the top vertex, and an exterior angle $y^\circ$ at the right base. 2. **Recall angle rules:** - The sum of angles in a triangle is always 180°. - An exterior angle of a triangle equals the sum of the two opposite interior angles. 3. **Find $x$:** For the right triangle, the angles are 40°, $x$, and the third interior angle (let's call it $z$). Since the triangles are connected on a horizontal line, the top angle of the left triangle (65°) and the top angle of the right triangle ($x$) form a straight line. Therefore, $$65^\circ + x^\circ = 180^\circ$$ 4. **Calculate $x$:** $$x = 180^\circ - 65^\circ = 115^\circ$$ 5. **Find $y$:** The exterior angle $y$ at the right base of the right triangle equals the sum of the two opposite interior angles, which are 40° and $x$. So, $$y = 40^\circ + x = 40^\circ + 115^\circ = 155^\circ$$ **Final answers:** $$x = 115^\circ$$ $$y = 155^\circ$$