In the figure below, lines d and f are parallel and the angle measures are as given. What is the value of x ?

Vertical angles are the angles opposite of each other that are created when two lines cross. Vertical angles are always equal. So, the angle vertical to the 35-degree angle also has a measure of 35 degrees. The supplement of the 120-degree angle has a measure of 60 degrees (all straight lines measure 180 degrees), so we then have a triangle with angles measuring 35, 60, and x degrees, as shown in the figure provided. Since the angles of a triangle add to 180 degrees, x = 180 − 35 – 60 = 85 degrees.