To find the measure of angle ∠YVX, we need to use the fact that the angles around point $V$ form a full circle, which sums up to 360°.

From the diagram, the following angles are given:

• ∠ZVY = 52°
• ∠WVZ = 36°
• ∠UVX = 43°

Since the angles around point $V$ must add up to 360°, we can use this equation:

$\text{∠YVX} + \text{∠ZVY} + \text{∠WVZ} + \text{∠UVX} = 360°$

Substituting the known values:

$\text{∠YVX} + 52° + 36° + 43° = 360°$

Now, simplify the right-hand side:

$\text{∠YVX} + 131° = 360°$

Solve for ∠YVX:

$\text{∠YVX} = 360° - 131° = 229°$

Finally, subtract ∠ZVY + ∠WVZ (since they share a line):

Answer: