1. **State the problem:** We are given a triangle with angles 26°, 34°, and 62°, and two unknown angles labeled $x^\circ$ and $y^\circ$. We need to find the measures of $x$ and $y$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. That is, $$26^\circ + 34^\circ + 62^\circ = 180^\circ$$ 3. **Calculate the sum of the given interior angles:** $$26 + 34 + 62 = 122^\circ$$ 4. **Find the missing interior angle $y$:** Since the sum must be 180°, $$y = 180^\circ - 122^\circ = 58^\circ$$ 5. **Find the exterior angle $x$:** The exterior angle $x$ is adjacent to the interior angle $y$. By the exterior angle theorem, the exterior angle equals the sum of the two opposite interior angles. Alternatively, since $x$ and $y$ are a linear pair, $$x + y = 180^\circ$$ So, $$x = 180^\circ - y = 180^\circ - 58^\circ = 122^\circ$$ **Final answers:** $$x = 122^\circ, \quad y = 58^\circ$$