Question

for △arq ≅ △bwt, solve for x.

Explanation:

Step1: Equate corresponding - sides (assume $AR = BW$)

Since $\triangle ARQ\cong\triangle BWT$, corresponding sides are equal. Let's assume $AR = BW$. So, $9x=2x + 3$.
Subtract $2x$ from both sides: $9x-2x=2x + 3-2x$.
$7x=3$.
$x=\frac{3}{7}$. But this might not be correct as we need to check other correspondences. Let's assume $AQ = BT$.
So, $5x-11=3x + 9$.

Step2: Solve the equation $5x-11=3x + 9$

Subtract $3x$ from both sides: $5x-3x-11=3x-3x + 9$.
$2x-11=9$.
Add 11 to both sides: $2x-11 + 11=9 + 11$.
$2x=20$.

Step3: Isolate $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{20}{2}$.
$x = 10$.

Answer:

$x = 10$