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To solve for \( m\angle XVW \), we can use the fact that the angles around point \( V \) form a full circle, which sums to \( 360^\circ \).

We are given:
- \( m\angle WVU = 36^\circ \)
- \( m\angle UVW = 76^\circ \)

Since \( m\angle XVW \) is the remaining part of the full circle, we can calculate it as follows:

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

Substituting the given values:

\[
m\angle XVW = 360^\circ - (36^\circ + 76^\circ)
\]
\[
m\angle XVW = 360^\circ - 112^\circ = 248^\circ
\]

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

Would you like more details or have any questions? Here are some related questions you might want to explore:

1. How do angles around a point add up to \(360^\circ\)?
2. What is the difference between interior and exterior angles in polygons?
3. How can you use the sum of angles in a triangle to find missing angles?
4. What are supplementary and complementary angles, and how do they differ?
5. How can you apply angle sum properties in different geometrical shapes?

**Tip**: Always check if the sum of angles around a point adds up to \(360^\circ\) when dealing with multiple angles!

Solve for m∠XVW given that m∠WVU = 36° and m∠UVW = 76°.

Learn how to solve for angle m∠XVW given m∠WVU = 36° and m∠UVW = 76° using the sum of angles around a point theorem. This geometry problem is suitable for students in Grades 7-9.

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