1. **State the problem:** We have two intersecting lines forming four angles. One angle is 59° and we need to find the measures of angles $x$ and $y$. 2. **Recall important rules:** - Vertical angles are equal. - Adjacent angles on a straight line sum to 180°. - Complementary angles sum to 90°. 3. **Find $x$:** Since $x$ is adjacent to 59° on a straight line, their sum is 180°. $$x + 59 = 180$$ $$x = 180 - 59$$ $$x = 121$$ 4. **Find $y$:** The small square indicates $y$ forms a right angle (90°) with the horizontal line. Since $x$ and $y$ are vertical angles, $y = x = 121$ is not possible because $y$ is adjacent to a right angle. Instead, $y$ is complementary to the 59° angle (since $y$ and 59° form a right angle). $$y + 59 = 90$$ $$y = 90 - 59$$ $$y = 31$$ 5. **Final answers:** $$x = 121^\circ$$ $$y = 31^\circ$$