In `DeltaABC,angleB=55^(@)` and `angleC=65^(@)`. Then the measure of an exterior angle of `angleA` can be .............

Options

A. `125^(@)`
B. `120^(@)`
C. `115^(@)`
D. `110^(@)`

Answer

To find the measure of an exterior angle of angle A in triangle ABC where angle B = 55° and angle C = 65°, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angles**: We are given:
- Angle B = 55°
- Angle C = 65°

2. **Calculate Angle A**:
- The sum of the angles in a triangle is always 180°.
- Therefore, we can find angle A using the formula:
\[ \text{Angle A} = 180° - (\text{Angle B} + \text{Angle C}) \]
- Substitute the values:
\[ \text{Angle A} = 180° - (55° + 65°) \]
- Calculate:
\[ \text{Angle A} = 180° - 120° = 60° \]

3. **Determine the Exterior Angle of Angle A**:
- The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- Therefore, the exterior angle of angle A (let's denote it as X) can be calculated as:
\[ X = \text{Angle B} + \text{Angle C} \]
- Substitute the values:
\[ X = 55° + 65° \]
- Calculate:
\[ X = 120° \]

4. **Conclusion**:
- The measure of the exterior angle of angle A is 120°.

### Final Answer:
The measure of an exterior angle of angle A can be **120°**.