#### Answer

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons}
\\\hline1 & \text{KM = 35} & \text{Given}
\\2 & \text{KL + LM = KM} & \text{Segment Addition Postulate}
\\3 & \text{2x - 5 + 2x = 35} & \text{Substitution Property}
\\4 & \text{4x - 5 = 35} & \text{Distributive Property}
\\5 & \text{4x = 40} & \text{Addition Property of Equality}
\\6 & \text{x = 10} & \text{Division Property of Equality}
\\7 & \text{KL = 2x - 5} & \text{Given}
\\8 & \text{KL = 2(10) - 5} & \text{Substitution Property}
\\9 & \text{KL = 15} & \text{Simplify}
\end{array}

#### Work Step by Step

Substitute the lengths shown in the diagram and solve for x.
Use the value that you found for x to find the length of $\overline{KL}$.