Answer
$AE = 20.6$
Work Step by Step
Theorem 6-7 states that if three or more parallel lines cut off congruent segments off of a transversal, then they will cut off congruent segments off of any transversal.
We see from the diagram that the transversal $\overline{BF}$ is cut off in equal segments by the three parallel lines. We can then deduce that line $AE$ is also a transversal that is cut off in congruent segments by the same three parallel lines. We now know that $AC$ is congruent to $CE$, so they both have a length of $10.3$.
We are asked to find the length of $\overline{AE}$. We can do this by adding the lengths of the two segments $\overline{AC}$ and $\overline{CE}$ together:
$AE = AC + CE$
Let's plug in what we know:
$AE = 10.3 + 10.3$
Add to solve for $AE$:
$AE = 20.6$
