Angles a and b are vertical. if the measure of angle a is seventy-nine degrees, what is the measure of angle b?

Vertical angles are angles opposite each other where two lines cross. They are called this because they share a vertex. 

For instance, in the attached diagram that I drew, ∠CEA and ∠BED are vertical angles. You may be able to tell visually that they are also congruent. 

If, as given, ∠B and ∠A are vertical, and m∠A = 79°, then since ∠A ≅ ∠B, m∠B = 79°.