AMC10 2012 10A, Problem 4

Let $\angle ABC = 24^\circ$ and $\angle ABD = 20^\circ$. What is the smallest possible degree measure for $\angle CBD$?

Solution: $\angle ABD$ and $\angle ABC$ share ray $AB$. In order to minimize the value of $\angle CBD$, $D$ should be located between $A$ and $C$. $\angle ABC = \angle ABD + \angle CBD$, so $\angle CBD = 4$. The answer is $\fbox{4}$

Answer: 4