Question

Solve for x. Show the equation you used and your work.

Answer 1

More information is needed to answer your question.

The answer provided below is on the assumption that |AD| is an angle bisector of <BAC, by Sine rule

$\frac{\sin{\angle BAD}}{24}=\frac{\sin{\angle BDA}}{36} \\ \\ \Rightarrow\sin{\angle BAD}=\frac{24\sin{\angle BDA}}{36}$

Also,
$\frac{\sin{\angle CAD}}{18}=\frac{\sin{\angle CDA}}{x} \\ \\ \Rightarrow\sin{\angle CAD}=\frac{18\sin{\angle CDA}}{x}$

But,
$\angle BAD=\angle CAD$

Thus,
$\frac{24\sin{\angle BDA}}{36}=\frac{18\sin{\angle CDA}}{x} \\ \\ x\sin{\angle BDA}=27\sin{\angle CDA}$

But, $\angle BDA\ and\ \angle CDA$ are supplementary angles, hence they are equal.

Therefore, x = 27