Theorems are a way for mathematicians to make a general mathematical statement. These statements can be used to help you solve all sorts of problems! See an introductions to theorems with this tutorial.
When two lines or segments intersect, two pairs of vertical angles are formed. By the Vertical Angle Theorem, vertical angles are congruent. If you have algebraic expressions for the measures of the vertical angles, you can use the Vertical Angle Theorem to solve for their measures. Check out the tutorial to learn more!