In a `Delta ABC`, the sum of exterior angles at B and C is equal to:

Options

A. `180^(@) - angle BAC`
B. `180^(@) + angle BAC`
C. `180^(@) - 2 angle BAC`
D. `180^(@) + 2 angle BAC`

Answer

To solve the question regarding the sum of the exterior angles at points B and C in triangle ABC, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Exterior Angles**:
- In triangle ABC, when we extend the sides at points B and C, we create two exterior angles: one at point B (let's call it angle ABD) and one at point C (let's call it angle ACE).

2. **Applying the Exterior Angle Theorem**:
- According to the exterior angle theorem, the exterior angle at a vertex of a triangle is equal to the sum of the two opposite interior angles.
- Therefore, we have:
- Angle ABD = Angle CAB + Angle ACB (for the exterior angle at B)
- Angle ACE = Angle ABC + Angle CAB (for the exterior angle at C)

3. **Summing the Exterior Angles**:
- Now, we can sum the two exterior angles:
- Angle ABD + Angle ACE = (Angle CAB + Angle ACB) + (Angle ABC + Angle CAB)

4. **Simplifying the Expression**:
- Combining the terms, we get:
- Angle ABD + Angle ACE = Angle CAB + Angle ACB + Angle ABC + Angle CAB
- This simplifies to:
- Angle ABD + Angle ACE = 2 * Angle CAB + Angle ACB + Angle ABC

5. **Using the Angle Sum Property**:
- The sum of the interior angles of triangle ABC is always 180 degrees:
- Angle CAB + Angle ABC + Angle ACB = 180 degrees

6. **Final Calculation**:
- Substituting the sum of the interior angles into our equation:
- Angle ABD + Angle ACE = 180 degrees + Angle CAB
- Therefore, the sum of the exterior angles at B and C is equal to:
- Angle ABD + Angle ACE = 180 degrees + Angle B

7. **Conclusion**:
- Hence, the sum of the exterior angles at B and C is equal to 180 degrees plus the angle at B.

### Final Answer:
The sum of the exterior angles at B and C is equal to \(180^\circ + \text{Angle B}\).

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