To solve for $y$ and find the missing angles in this triangle, we’ll proceed as follows:

Step 1: Set up the equation for $y$

Since $\triangle WYX$ is a triangle, the sum of its interior angles must be $180^\circ$. The three angles are:

1. $\angle W = (4y - 4)^\circ$
2. $\angle ZYX = 52^\circ$
3. $\angle X = (3y)^\circ$

So, we set up the equation: $(4y - 4) + 52 + 3y = 180$

Step 2: Solve for $y$

Combine like terms: $7y + 48 = 180$ Subtract 48 from both sides: $7y = 132$ Now, divide by 7: $y = 18.857 \approx 19$

Step 3: Substitute $y$ to find the angles

1. Calculate $\angle W$: [ \angle W = 4y - 4 = 4(18.857) - 4 = 75.428