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The diagram shows three angles formed at point W: \(\angle VWY\), \(\angle XWY\), and \(\angle VWX\). You're asked to solve for \(m\angle VWY\), and we are given two of the angles:

- \(\angle XWY = 39^\circ\) (blue angle),
- \(\angle VWX = 69^\circ\) (red angle).

Since \(\angle VWY\) is part of the larger angle formed by \(\angle VWX\), we can use the following property of adjacent angles around a point:

\[
m\angle VWX = m\angle VWY + m\angle XWY
\]

Substituting the known values:

\[
69^\circ = m\angle VWY + 39^\circ
\]

To find \(m\angle VWY\), subtract \(39^\circ\) from both sides:

\[
m\angle VWY = 69^\circ - 39^\circ = 30^\circ
\]

Therefore, \(m\angle VWY = 30^\circ\).

Would you like more details or have any questions?

Here are some related questions:
1. What is the definition of adjacent angles?
2. How do you calculate the sum of angles around a point?
3. What is the difference between interior and exterior angles?
4. How would you approach a situation with three or more angles at a point?
5. How do angle relationships change when dealing with parallel lines?

**Tip**: In geometry, always check if the angles are adjacent or form a straight line to apply the correct sum properties.

Learn how to solve for angle VWY using adjacent angles and the angle sum property. The problem gives two known angles, ∠XWY = 39° and ∠VWX = 69°, and uses the formula to find m∠VWY. Suitable for students in Grades 6-8.

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