Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle.

Explanation

To prove that the angle between the internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Triangle and Angles**:
Let triangle ABC be given, where angle A is the vertex angle, and angles B and C are the base angles. The internal bisector of angle B is BE, and the external bisector of angle C is CE.

2. **Understand the Vertical Angle**:
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