1. **Problem Statement:** We have two intersecting lines forming angles. One angle is given as 34°. Angle $x$ is marked as a right angle, so $x = 90^\circ$. We need to find the measure of the missing angle $y$. 2. **Key Concepts:** - Vertical angles are equal. - Adjacent angles on a straight line sum to 180°. - Complementary angles sum to 90°. 3. **Analyze the figure:** Since $x$ is a right angle, $x = 90^\circ$. Angle $y$ is adjacent to $x$ and together they form a straight line with the 34° angle on the other side. 4. **Calculate $y$:** The straight line angle sum is 180°, so $$x + y = 180^\circ$$ Substitute $x = 90^\circ$: $$90^\circ + y = 180^\circ$$ Subtract 90° from both sides: $$\cancel{90^\circ} + y = 180^\circ - \cancel{90^\circ}$$ $$y = 90^\circ$$ 5. **Final answers:** $$x = 90^\circ$$ $$y = 90^\circ$$