Question 7 of 10 Which is the best definition of an exterior angle of a triangle? A. An angle that is formed by two segments that are sides of the triangle B. An angle that forms a linear pair with one of the interior angles of the triangle C. An angle that is formed by two segments that are not sides of the triangle D. An angle that is complementary to one of the interior angles of the triangle

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UpStudy AI · Accepted Answer

The **best definition of an exterior angle of a triangle** is:

**B. An angle that forms a linear pair with one of the interior angles of the triangle**

### **Explanation:**

An **exterior angle** of a triangle is formed when one side of the triangle is extended beyond one of its vertices. Specifically, it is the angle adjacent to the interior angle, and together they form a **linear pair**, meaning they are supplementary and add up to 180 degrees.

Here's a breakdown of each option:

- **A. An angle that is formed by two segments that are sides of the triangle**
  - **Incorrect.** This describes an **interior angle** of the triangle, not an exterior one.

- **B. An angle that forms a linear pair with one of the interior angles of the triangle**
  - **Correct.** This accurately describes an exterior angle, as it is supplementary to an adjacent interior angle.

- **C. An angle that is formed by two segments that are not sides of the triangle**
  - **Incorrect.** This does not specifically relate to the exterior angles of the triangle.

- **D. An angle that is complementary to one of the interior angles of the triangle**
  - **Incorrect.** Complementary angles add up to 90 degrees, whereas an exterior and its adjacent interior angle add up to 180 degrees.

### **Visual Representation:**

Consider triangle **ABC**:

```
       A
      / \
     /   \
    B-----C
```

If you extend side **BC** beyond **C** to a point **D**, the **exterior angle** at **C** is the angle formed between **AC** and **CD**. This exterior angle and the interior angle at **C** (angle **ACB**) form a linear pair, summing to 180 degrees.

### **Conclusion:**

Option **B** precisely captures the essence of what defines an exterior angle in a triangle by highlighting its relationship with the interior angle through a linear pair.
An exterior angle of a triangle is an angle that forms a linear pair with one of the interior angles of the triangle.

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