solve for $x$. figures are not necessarily drawn to scale.

Explanation:

Step1: Identify similar triangles

$\angle K = \angle N = 97^\circ$, $\angle KLJ = \angle NLM$ (vertical angles), so $\triangle KLJ \sim \triangle NLM$ by AA similarity.

Step2: Set up proportion of sides

Corresponding sides are proportional: $\frac{KJ}{MN} = \frac{KL}{NL}$ Substitute values: $\frac{x}{8} = \frac{9.8}{5.6}$

Step3: Solve for $x$

Multiply both sides by 8: $x = 8 \times \frac{9.8}{5.6}$ Calculate $\frac{9.8}{5.6} = 1.75$, then $x = 8 \times 1.75$

Answer:

14