Đáp án:
$\begin{array}{l}
a)AN + NC = AC\\
\Leftrightarrow NC = 8,5 - 5 = 3,5\\
MN//BC\\
\Leftrightarrow \dfrac{{AM}}{{BM}} = \dfrac{{AN}}{{CN}}\left( {theo\,Talet} \right)\\
\Leftrightarrow \dfrac{4}{x} = \dfrac{5}{{3,5}}\\
\Leftrightarrow x = \dfrac{{4.3,5}}{5} = 2,8\\
Vậy\,x = 2,8\\
b)DQ + QF = DF\\
\Leftrightarrow DQ = 24 - 9 = 15\\
Do:PQ//EF\\
\Leftrightarrow \dfrac{{DP}}{{PE}} = \dfrac{{DQ}}{{QF}}\left( {theo\,Talet} \right)\\
\Leftrightarrow \dfrac{x}{{10,5}} = \dfrac{{15}}{9} = \dfrac{5}{3}\\
\Leftrightarrow x = \dfrac{5}{3}.10,5 = 17,5\\
Vậy\,x = 17,5
\end{array}$
