1. **Stating the problem:** We are given a geometric figure with two parallel horizontal lines and two pairs of parallel slanted lines forming a central triangle-like shape. The angles 62° and 50° are given at the top-left and bottom-left intersections respectively. We need to find the angles $x$ (bottom-right) and $y$ (top apex). 2. **Key properties and formulas:** - Alternate interior angles formed by parallel lines are equal. - The sum of angles in a triangle is $180^\circ$. - Angles on a straight line sum to $180^\circ$. 3. **Find angle $y$ at the top apex:** Since the top-left angle is $62^\circ$ and the top and bottom horizontal lines are parallel, the angle adjacent to $y$ on the top line is also $62^\circ$ (alternate interior angles). The top apex angle $y$ and this $62^\circ$ angle form a straight line, so: $$y + 62^\circ = 180^\circ$$ $$y = 180^\circ - 62^\circ = 118^\circ$$ 4. **Find angle $x$ at the bottom-right:** The bottom-left angle is $50^\circ$. Because the left and right slanted lines are parallel, the angle corresponding to $x$ on the bottom line is also $50^\circ$ (alternate interior angles). The angles inside the triangle formed by the central slanted lines and the bottom horizontal line are $x$, $50^\circ$, and $y$ (already found as $118^\circ$). The sum of these angles is $180^\circ$: $$x + 50^\circ + 118^\circ = 180^\circ$$ $$x + 168^\circ = 180^\circ$$ $$x = 180^\circ - 168^\circ = 12^\circ$$ **Final answers:** $$x = 12^\circ$$ $$y = 118^\circ$$