https://file.aiquickdraw.com/mathbot/file/1727448456264ahhw27cq.jpg

To solve for \( m \angle XVW \) in the provided image, we can use the properties of angles around a point. The sum of angles around a point (at vertex \( V \)) is \( 360^\circ \).

From the diagram:
- \( m \angle UVW = 36^\circ \)
- \( m \angle WVU = 76^\circ \)

Thus, the remaining angle \( m \angle XVW \) can be calculated as:

\[
m \angle XVW = 360^\circ - (m \angle UVW + m \angle WVU)
\]

Now, substituting the given values:

\[
m \angle XVW = 360^\circ - (36^\circ + 76^\circ)
\]

\[
m \angle XVW = 360^\circ - 112^\circ = 248^\circ
\]

Therefore, \( m \angle XVW = 248^\circ \).

Would you like further details or have any additional questions?

Here are some related questions to explore:
1. How do we calculate the sum of interior angles in a polygon?
2. What is the relationship between angles around a point?
3. How do we classify angles based on their measurements?
4. What is an exterior angle, and how is it related to interior angles?
5. How can we calculate unknown angles using algebraic methods?

**Tip**: When working with angles around a point, always remember that their sum is \( 360^\circ \).

Learn how to solve for angle XVW using the property of the sum of angles around a point. The problem provides angles UVW and WVU, and you will calculate the missing angle XVW. Suitable for students in Grades 7-9.

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