2012 AMC 10A Problem 4

Question

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

Both angles share ray

BA

The smallest angle occurs when the two given angles overlap as much as possible

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.

Problem 4 in other years