Question

if $overline{ux}congoverline{wx}$, $mangle uvx = z + 40^{circ}$, and $mangle wvx = 3z$, what is the value of $z$?
$z=square^{circ}$

Explanation:

Step1: Use congruent - side property

Since $\overline{UX}\cong\overline{WX}$, and $\angle U$ and $\angle W$ are right - angles, and $\overline{VX}$ is common, triangles $\triangle UVX$ and $\triangle WVX$ are congruent by the Hypotenuse - Leg (HL) congruence theorem. Then $\angle UVX=\angle WVX$.

Step2: Set up the equation

Set up the equation $z + 40=3z$.

Step3: Solve the equation

Subtract $z$ from both sides: $40=3z - z$. So, $40 = 2z$.
Divide both sides by 2: $z=\frac{40}{2}=20$.

Answer:

$20$