Question

what is the value of z?
z = \boxed{2}

Explanation:

Step1: Identify congruent triangles

Since $JB=BK$, $\angle MBJ=\angle MBK=90^\circ$, and $MB$ is shared, $\triangle MBJ \cong \triangle MBK$ by SAS. Thus, $MJ=MK$.

Step2: Set up equation for equal sides

$8z - 24 = 2z$

Step3: Isolate z term

Subtract $2z$ from both sides:
$8z - 2z - 24 = 0$
$6z - 24 = 0$

Step4: Solve for z

Add 24 to both sides, then divide by 6:
$6z = 24$
$z = \frac{24}{6} = 4$

Answer:

$z=4$