We are asked to find the size of angle $x$ in the given diagram. The diagram shows a straight line, and two other lines intersecting at a point on it. The angle between one of these lines and the straight line is $20^{\circ}$, and the angle between the other line and the straight line is $65^{\circ}$. The angle $x$ is the angle between these two lines.

1. Problem Description

We are asked to find the size of angle $x$ in the given diagram. The diagram shows a straight line, and two other lines intersecting at a point on it. The angle between one of these lines and the straight line is $20^{\circ}$, and the angle between the other line and the straight line is $65^{\circ}$. The angle $x$ is the angle between these two lines.

2. Solution Steps

Since the angles lie on a straight line, the sum of the angles on one side of the straight line is $180^{\circ}$. The angle $x$ along with the two given angles, $20^{\circ}$ and $65^{\circ}$ add up to $180^{\circ}$.

We can write the equation:

$x + 20^{\circ} + 65^{\circ} = 180^{\circ}$

Combining the known angles:

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

Subtracting $85^{\circ}$ from both sides of the equation gives us the value of $x$:

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

$x = 95^{\circ}$

3. Final Answer

$x = 95^{\circ}$