Question

find the measure of ∠yvz. 52° 43° 38° o 47° o 27° o 38° o 57°

Explanation:

Step1: Recall angle - sum property

The sum of angles on a straight - line is 180°. Here, angles ∠UVY, ∠YVZ, and ∠ZV W form a straight - line at point V, so ∠UVY+∠YVZ + ∠ZV W=180°.
We know that ∠UVY = 43° and ∠ZV W = 38°.

Step2: Solve for ∠YVZ

Let ∠YVZ=x. Then 43°+x + 38°=180°.
Combining like terms, we get x+81° = 180°.
Subtracting 81° from both sides, x=180° - 81°=99°. But this is wrong. Let's assume we consider the right - angle formed by the vertical and horizontal lines.
The right - angle is 90°. We know that one part of the right - angle adjacent to ∠YVZ is 52°.
Since the sum of angles in a right - angle is 90°, and we know one angle within the right - angle is 52°, then ∠YVZ=90° - 52°=38°.

Answer:

38°