Polygon \( \mathrm{ABCD} \cong \) Polygon JKLM \[ \begin{array}{l}\mathrm{AC}=10 \mathrm{x}+6 \\ \mathrm{JL}=9 \mathrm{x}+17\end{array} \] Find the value of x and JL. Provide answers accurate to the nearest hundredth.

To solve for \( x \) and \( JL \), we start with the information given about the congruent polygons \( \mathrm{ABCD} \) and \( \mathrm{JKLM} \). Since the polygons are congruent, the corresponding sides are equal. Therefore, we can set up the equation: \[ AC = JL \] Substituting the expressions for \( AC \) and \( JL \): \[ 10x + 6 = 9x + 17 \] Now, we will solve for \( x \) step by step. 1. **Isolate \( x \)**: - Subtract \( 9x \) from both sides: \[ 10x - 9x + 6 = 17 \] This simplifies to: \[ x + 6 = 17 \] 2. **Subtract 6 from both sides**: \[ x = 17 - 6 \] Thus, we find: \[ x = 11 \] Now that we have the value of \( x \), we can substitute it back into the expression for \( JL \): \[ JL = 9x + 17 \] Substituting \( x = 11 \): \[ JL = 9(11) + 17 \] Calculating this gives: \[ JL = 99 + 17 = 116 \] Thus, the final answers are: - The value of \( x \) is \( 11 \). - The value of \( JL \) is \( 116 \). Both answers are accurate to the nearest hundredth, though they are whole numbers. Final results: - \( x = 11 \) - \( JL = 116 \)