We are asked to find the size of angle $x$ in the given diagram. We are given that the angles $30^{\circ}$, $x$, and $55^{\circ}$ lie on a straight line.

1. Problem Description

We are asked to find the size of angle $x$ in the given diagram. We are given that the angles $30^{\circ}$, $x$, and $55^{\circ}$ lie on a straight line.

2. Solution Steps

Angles on a straight line add up to $180^{\circ}$. Therefore, the sum of the angles $30^{\circ}$, $x$, and $55^{\circ}$ is equal to $180^{\circ}$.

We can write this as an equation:

$30^{\circ} + x + 55^{\circ} = 180^{\circ}$

Combining the known angles:

$85^{\circ} + x = 180^{\circ}$

To solve for $x$, we subtract $85^{\circ}$ from both sides of the equation:

$x = 180^{\circ} - 85^{\circ}$

$x = 95^{\circ}$

3. Final Answer

The size of angle $x$ is $95^{\circ}$.