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To find the angle \(XYW\) in the triangle, we can use the Law of Sines or the Law of Cosines. Given:

- \(WX = 7 \, \text{cm}\)
- \(WY = 8 \, \text{cm}\)
- Angle \(WXY = 65^\circ\)

We are looking for the angle \(XYW\).

### Step-by-Step Solution

We will use the Law of Sines, which states:

\[
\frac{\sin(\text{Angle})}{\text{Opposite Side}} = \frac{\sin(\text{Another Angle})}{\text{Opposite Side to That Angle}}
\]

Let's denote:
- \( \angle WXY = 65^\circ \)
- \( WX = 7 \, \text{cm} \)
- \( WY = 8 \, \text{cm} \)

We need to find \( \angle XYW \).

By the Law of Sines:

\[
\frac{\sin(XYW)}{WX} = \frac{\sin(WXY)}{WY}
\]

Substitute the known values:

\[
\frac{\sin(XYW)}{7} = \frac{\sin(65^\circ)}{8}
\]

Now, solve for \( \sin(XYW) \):

\[
\sin(XYW) = 7 \times \frac{\sin(65^\circ)}{8}
\]

Calculate \( \sin(65^\circ) \):

\[
\sin(65^\circ) \approx 0.9063
\]

Substitute this value:

\[
\sin(XYW) \approx 7 \times \frac{0.9063}{8} \approx 7 \times 0.1133 \approx 0.7931
\]

Now, find \( XYW \):

\[
XYW = \arcsin(0.7931)
\]

\[
XYW \approx 52.4^\circ
\]

### Final Answer

\[
\boxed{52.4^\circ}
\]

Would you like further details or have any questions?

### Related Questions:
1. How would the solution change if one of the sides were different?
2. Can the Law of Cosines also be used to solve for angle \(XYW\)?
3. What is the measure of the third angle, \(WYX\), in this triangle?
4. How do you compute the area of triangle \(WXY\) using trigonometric functions?
5. What other properties can be derived from the triangle given?

### Tip: 
Always check if the angle is acute or obtuse when using the inverse sine function to avoid any mistakes in calculation.

Learn how to find the angle XYW in a triangle using the Law of Sines. Given the sides WX = 7 cm, WY = 8 cm, and angle WXY = 65°, follow a step-by-step solution suitable for Grades 9-11 students.

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