[ Measurement of segment lengths and angle measures. Adjacent angles.]

On a straight line, four points $A, B, C$, and $D$ are chosen, such that $A B=1, B C=2, C D=4$. What can $A D$ be equal to?
Consider all possible cases of the arrangement of these points.

## Solution

First, let's determine what the distance between points $A$ and $C$ can be. If point $B$ is located on the segment $A C$, then $A C = 3$. If point $B$ is outside $A C$, then $A C = 1$.

Now we have two problems: in one, $A C = 3$ and $C D = 4$, and in the other, $A C = 1$ and $C D = 4$. Each of these problems gives two possibilities, so there are a total of four possibilities: $4 + 3 = 7$, $4 - 3 = 1$, $4 + 1 = 5$, $4 - 1 = 3$.

## Answer

$1, 3, 5$ or 7.