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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!

Find the measure of angle WYZ given that angle WYX is 45° and angle XYZ is 40°.

This problem involves finding the measure of angle WYZ using the exterior angle theorem. Given that angle WYX is 45° and angle XYZ is 40°, the solution involves applying the theorem to calculate the exterior angle. Suitable for students in Grades 8-10.

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