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

2012 AMC 10A Problem 4 — Solution

Attempt Problem 4 of the 2012 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

$0$

$2$

$4$

$6$

$12$

Note that both of the angles share the ray $AB.$ To minimize the desired degree, we want $D$ to be between $A$ and $C.$

This would make $\begin{aligned} \angle CBD &= \angle ABC - \angle ABD \\ &= 4^{\circ}. \end{aligned}$

Thus, C is the correct answer.