∡ 94° and ∡ 82° are vertical angles, meaning that the opposite side is the same angle as them. We will need this info later on.
The angle to the left of ∡ 94° is empty, and notice how that angle plus ∡ 94° creates a straight line, and a straight line equals 180°.
So, 180 - 94 = 86°
The correspondent angle of ∡ 86 on that transversal is in that little triangle. The line where ∡ 82 is located with x on the inside creates a little triangle within the big triangle, and the angles in a triangle always add up to 180°.
One side of that triangle is x, another side is 86°, and according to vertical angles, the vertical opposite angle of ∡ 82° lies inside that triangle so our other angle is 82°.
Since the angles of triangles add up to 180,
x + 82 + 86 = 180°
x + 168 = 180
- 168 - 168
x + 0 = 12°
Therefore, x = 12° :) I'm sorry if all the text hurts your eyes.