Question

if ∠uwv ≅ ∠uwx, uv = 4y, and ux = y + 72, what is the value of y?
(there is a diagram with points u, w, x, v and right angles at x and v)

Explanation:

Step1: Identify congruent segments

Since $\angle UWV \cong \angle UWX$ and $WX \perp UX$, $WV \perp UV$ (right angles), by Angle - Angle - Side (AAS) or Hypotenuse - Leg (HL) congruence, $UV = UX$.

Step2: Set up the equation

Given $UV = 4y$ and $UX=y + 72$, set them equal: $4y=y + 72$.

Step3: Solve for y

Subtract $y$ from both sides: $4y-y=y + 72-y\Rightarrow3y = 72$.
Divide both sides by 3: $y=\frac{72}{3}=24$.

Answer:

24