Question

what is this value of x?

Explanation:

Step1: Find the alternate - interior angle

The alternate - interior angle to the $105^{\circ}$ angle is also $105^{\circ}$ because alternate - interior angles between parallel lines are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is $180^{\circ}$. Let the angle we want to find be $x$. In the triangle formed, one angle is $105^{\circ}$, and we assume the other non - $x$ angle is also $105^{\circ}$ (due to parallel lines and angle relationships). Then $x=105^{\circ}+105^{\circ}- 180^{\circ}$.
$x = 30^{\circ}$

Answer:

$30$