What is the value of w?

The correct answer is 57 degrees.

Step-by-step explanation:

To solve this problem, we need to remember the concept of vertical angles.  When two angles are directly across from each other, like angle w and the angle that measures 57 degrees in the diagram, they are known as vertical angles.  Vertical angles always have the same measure.  Therefore, we can conclude that angle w must also measure 57 degrees.

Hope this helps!