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To classify the triangle with angles measuring \(55^\circ\), \(60^\circ\), and \(65^\circ\), let's analyze it:

1. **Triangle Sum Property**: The sum of the interior angles of any triangle is \(180^\circ\). Here:
   \[
   55^\circ + 60^\circ + 65^\circ = 180^\circ
   \]
   Thus, it is indeed a triangle.

2. **Types Based on Angles**:
   - **Acute Triangle**: All angles are less than \(90^\circ\). Since \(55^\circ\), \(60^\circ\), and \(65^\circ\) are all acute angles, this triangle is an **acute triangle**.
   - **Scalene Triangle**: All three angles are different (\(55^\circ \neq 60^\circ \neq 65^\circ\)), meaning all sides have different lengths. Therefore, this triangle is also a **scalene triangle**.

### Final Classification:
This triangle is both an **acute triangle** and a **scalene triangle**.

Would you like further clarification or examples? Here are some questions for expansion:

1. What defines other types of triangles based on angles, such as obtuse or right triangles?
2. How can the side lengths of this scalene triangle be determined using trigonometric relationships?
3. What are the key characteristics of an isosceles triangle, and how do they differ from a scalene triangle?
4. How can we verify that a triangle is acute if the angles are given algebraically?
5. What is the importance of the triangle sum property in solving geometry problems?

**Tip**: Always double-check that the sum of angles equals \(180^\circ\) when classifying triangles to avoid errors.

If the angles of a triangle measure 55°, 60°, and 65°, then what two names describe the type of triangle it is? Explain how you know.

Discover how to classify a triangle with angles measuring 55°, 60°, and 65°. This detailed solution explains the classification as an acute scalene triangle using the triangle sum property and angle analysis. Perfect for students in Grades 6-8.

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