Final answer:
Two vertical angles are always equal in measure, so if one angle measures 39 degrees, the other angle also measures 39 degrees.
Step-by-step explanation:
If two angles are vertical angles, they are opposite each other where two lines intersect and are always equal in measure. Knowing this, if one vertical angle measures 39 degrees, the other vertical angle must also measure 39 degrees. It is important to note that angles can be further broken down into minutes of arc and seconds of arc. However, in this case, we are only concerned with the degrees measure of the angle.