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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: 

Find the measure of ∠YVX. Given: ∠ZVY = 52°, ∠WVZ = 36°, ∠UVX = 43°.

This problem demonstrates how to find the measure of ∠YVX using angle relationships around a point. Given the angles ∠ZVY = 52°, ∠WVZ = 36°, and ∠UVX = 43°, the solution involves subtracting the sum of known angles from 360°. Suitable for students in Grades 8-10.

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