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To solve this problem, we need to determine the justification for the measure of angle \( \angle SVU = 115^\circ \) based on the given information.

### Given:
- \( \triangle SUV \)
- \( m\angle S = 15^\circ \)
- \( m\angle U = 50^\circ \)

### To Prove:
- \( m\angle SVU = 115^\circ \)

### Solution:
In any triangle, the sum of the interior angles is \( 180^\circ \). Therefore, for \( \triangle SUV \):
\[
m\angle S + m\angle U + m\angle SVU = 180^\circ
\]

We know:
\[
m\angle S = 15^\circ \quad \text{and} \quad m\angle U = 50^\circ
\]

Substitute the values:
\[
15^\circ + 50^\circ + m\angle SVU = 180^\circ
\]

Simplify by adding the known angles:
\[
65^\circ + m\angle SVU = 180^\circ
\]

Subtract \( 65^\circ \) from both sides to solve for \( m\angle SVU \):
\[
m\angle SVU = 180^\circ - 65^\circ = 115^\circ
\]

### Justification:
This result is justified by the **Triangle Angle Sum Theorem**, which states that the sum of the interior angles of a triangle is always \( 180^\circ \).

### Conclusion:
The measure of \( m\angle SVU \) is \( 115^\circ \), and the reasoning is based on the Triangle Angle Sum Theorem.

---

Would you like more details on this solution or have any other questions? Here are some related questions to explore further:

1. What are some examples of other triangle properties and theorems?
2. How can the Triangle Angle Sum Theorem be applied in different types of triangles?
3. What are the properties of exterior angles in triangles?
4. How would this problem change if \( \triangle SUV \) were not a typical triangle but an obtuse or right triangle?
5. What are some real-world applications of the Triangle Angle Sum Theorem?

**Tip:** Remember, the Triangle Angle Sum Theorem is a fundamental tool in geometry, applicable to all triangles regardless of type.

From this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. Given: ∆SUV, m∠S = 15, and m∠U = 50. Prove: m∠SVU = 115.

Learn how to use the Triangle Angle Sum Theorem to find the measure of angle SVU in triangle SUV given m∠S = 15 and m∠U = 50. This problem involves key geometry concepts and is suitable for Grades 8-10.

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