1. **Stating the problem:** We have two intersecting lines forming a right angle (90°) and an angle of 68° marked between the lower left and upper right arms. 2. **Identify the angles:** The right angle is between angles $x$ and $y$, so $x$ and $y$ are complementary angles because they add up to 90°. 3. **Use the property of vertical angles:** The angle opposite the 68° angle is also 68° because vertical angles are equal. 4. **Calculate angle $x$:** Since $x$ and the 68° angle are on a straight line, they add up to 180°. $$x + 68 = 180$$ 5. **Solve for $x$:** $$x = 180 - 68 = 112$$ 6. **Calculate angle $y$:** Since $x$ and $y$ are complementary, $$x + y = 90$$ Substitute $x = 112$: $$112 + y = 90$$ 7. **Solve for $y$:** $$y = 90 - 112 = -22$$ This negative value indicates a misinterpretation; actually, $x$ and $y$ form the right angle, so $x + y = 90$. Since $x = 68$ (vertical angle), then: $$y = 90 - 68 = 22$$ **Final answers:** $$x = 68^\circ$$ $$y = 22^\circ$$