Exterior angle of a triangle is always ____ then either of its interior opposite angles .

Answer

To solve the question, "Exterior angle of a triangle is always ____ than either of its interior opposite angles," we need to establish the relationship between the exterior angle and the interior opposite angles of a triangle.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- Let's denote a triangle as \( \triangle ABC \).
- The vertices of the triangle are labeled as \( A \), \( B \), and \( C \).

2. **Identifying the Exterior Angle**:
- Extend one side of the triangle, say side \( BC \), beyond point \( C \).
- The angle formed outside the triangle at vertex \( C \) is called the exterior angle. Let's denote this exterior angle as \( \angle ACD \).

3. **Identifying the Interior Opposite Angles**:
- The interior opposite angles to the exterior angle \( \angle ACD \) are \( \angle ABC \) and \( \angle BAC \).
- These angles are located inside the triangle and are opposite to the exterior angle.

4. **Using the Exterior Angle Theorem**:
- According to the Exterior Angle Theorem, the exterior angle \( \angle ACD \) is equal to the sum of the two opposite interior angles:
\[ \angle ACD = \angle ABC + \angle BAC \]

5. **Establishing the Relationship**:
- Since both \( \angle ABC \) and \( \angle BAC \) are positive angles, it follows that:
\[ \angle ACD > \angle ABC \quad \text{and} \quad \angle ACD > \angle BAC \]
- Therefore, we conclude that the exterior angle \( \angle ACD \) is always greater than either of the interior opposite angles.

6. **Filling in the Blank**:
- Based on the above reasoning, we can fill in the blank in the statement:
"Exterior angle of a triangle is always **greater** than either of its interior opposite angles."

### Final Answer:
The exterior angle of a triangle is always **greater** than either of its interior opposite angles.