To find the measure of $\angle WYZ$, let's analyze the diagram.

• We are given that $\angle WYX = 45^\circ$ and $\angle XYZ = 40^\circ$.
• $\angle WYZ$ is the exterior angle for $\triangle WXY$.

Using the exterior angle theorem, which states that an exterior angle is equal to the sum of the two non-adjacent interior angles:

$m\angle WYZ = m\angle WYX + m\angle XYZ = 45^\circ + 40^\circ = 85^\circ$

Thus, the measure of $\angle WYZ$ is 85°, which corresponds to option C.

Would you like further explanation or details? Here are some related questions to deepen your understanding:

1. What is the exterior angle theorem?
2. How do you calculate angles in a triangle?
3. Why are the sum of the angles in any triangle always 180°?
4. How can you determine missing angles in different types of triangles (like isosceles or right triangles)?
5. Can the exterior angle theorem be used with polygons other than triangles?

Tip: The exterior angle theorem is very useful when working with triangles—remember that it applies to any triangle shape!