solve for $x$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to…

solve for $x$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

solve for $x$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Answer

Explanation:

Step1: Confirm similar triangles

Triangles $\triangle LMN$ and $\triangle OPQ$ have identical angle measures ($39^\circ, 58^\circ, 83^\circ$), so they are similar by AA similarity. Corresponding sides: $MN \leftrightarrow PO$, $LM \leftrightarrow QP$.

Step2: Set up proportion

Match corresponding sides: $\frac{x}{11} = \frac{29}{17}$

Step3: Solve for x

Multiply both sides by 11: $x = 11 \times \frac{29}{17}$ Calculate the value: $x = \frac{319}{17} \approx 18.8$

Answer:

$18.8$