Find the measure of YVZ

47°

Explanation:

Line UVW is a straight line. This means it must have a measure of 180°. As you can see in the diagram, <UVX, <XVY, <YVZ, and <ZVW also split <UVW into four different angles. By this logic, we know:

<UVX +  <XVY + <YVZ + <ZVW = 180°

Now, let's add in the values of the known angle measures and let x represent <YVZ in this equation:

43 + 52 + x + 38 = 180

133 + x = 180

x = 47

So, m<YVZ = 47°.