We are given a diagram with two parallel lines intersected by two transversals. We need to find the value of $x + y$.

1. Problem Description

We are given a diagram with two parallel lines intersected by two transversals. We need to find the value of $x + y$.

2. Solution Steps

Since the two horizontal lines are parallel, we can use properties of angles formed by parallel lines and transversals.

The angle vertically opposite to $35^{\circ}$ is also $35^{\circ}$. Since this $35^{\circ}$ angle and $y$ are supplementary angles, we have:

$y + 35^{\circ} = 180^{\circ}$

$y = 180^{\circ} - 35^{\circ}$

$y = 145^{\circ}$

The angle vertically opposite to $110^{\circ}$ is also $110^{\circ}$. Since this $110^{\circ}$ angle and $x$ are supplementary angles, we have:

$x + 110^{\circ} = 180^{\circ}$

$x = 180^{\circ} - 110^{\circ}$

$x = 70^{\circ}$

Now we can calculate $x+y$:

$x + y = 70^{\circ} + 145^{\circ} = 215^{\circ}$

3. Final Answer

$x + y = 215^{\circ}$

The answer is A.