what is the value of s? s =

Explanation:

Step1: Identify congruent triangles

Triangles $\triangle GFE$ and $\triangle GHE$ are congruent by the Hypotenuse - Angle (HA) congruence criterion (right - angles at $F$ and $H$ and $\angle FGE=\angle HGE = 41^{\circ}$, and they share side $GE$). So, $FE = HE$.

Step2: Set up the equation

Since $FE=6s - 59$ and $HE = 2s+9$, we set up the equation $6s-59=2s + 9$.

Step3: Solve the equation for $s$

Subtract $2s$ from both sides: $6s-2s-59=2s-2s + 9$, which simplifies to $4s-59=9$. Add 59 to both sides: $4s-59 + 59=9 + 59$, so $4s=68$. Divide both sides by 4: $\frac{4s}{4}=\frac{68}{4}$, then $s = 17$.

Answer:

$17$