1. **State the problem:** We have two vertical parallel lines cut by a transversal. Given angles 30°, 134°, and 110° on the left line, and angles $x^\circ$ and $y^\circ$ on the right line, we need to find $x$ and $y$. 2. **Recall important rules:** - Corresponding angles between parallel lines are equal. - Alternate interior angles between parallel lines are equal. - Linear pairs sum to 180°. 3. **Analyze the left line:** - The angle adjacent to the transversal is 134°. - The angle below it is 110°. - Since 134° and 110° are adjacent angles on a straight line, their sum should be 180° if they form a linear pair. Check sum: $$134 + 110 = 244 \neq 180$$ so these two are not adjacent on a straight line; likely 134° is an exterior angle and 110° is an interior angle. 4. **Find $y$:** - $y^\circ$ is adjacent to the transversal on the right vertical line. - Since the lines are parallel, the angle adjacent to the transversal on the right line corresponds to the angle adjacent to the transversal on the left line, which is 134°. - Therefore, $$y = 134$$ 5. **Find $x$:** - $x^\circ$ is diagonally opposite to $y^\circ$ on the right line. - Vertically opposite angles are equal. - So, $$x = y = 134$$ 6. **Final answers:** $$x = 134^\circ, \quad y = 134^\circ$$