1. **State the problem:** We have four intersecting lines forming two pairs of parallel lines cut by two transversals, creating angles 49° and 58° at the top left, and unknown angles $x$ (top right) and $y$ (bottom right). We need to find $x$ and $y$. 2. **Use angle relationships:** When two parallel lines are cut by a transversal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to 180°). 3. **Find $x$:** The angles 49° and 58° are adjacent and form a straight line, so their sum is 180°. $$49 + 58 + x = 180$$ Simplify: $$107 + x = 180$$ Subtract 107 from both sides: $$x = 180 - 107$$ $$x = 73$$ 4. **Find $y$:** Since $y$ is vertically opposite to $x$, vertical angles are equal. $$y = x = 73$$ **Final answers:** $$x = 73^\circ$$ $$y = 73^\circ$$