In `DeltaABC,angleA=70^(@)` and `angleB=60^(@)`. Then the measure of an exterior angle of `DeltaABC` can be ............

Options

A. `50^(@)`
B. `110^(@)`
C. `100^(@)`
D. `70^(@)`

Answer

To solve the problem, we need to find the measure of the exterior angles of triangle ABC where angle A = 70° and angle B = 60°.

### Step-by-Step Solution:

1. **Identify the Given Angles**:
- Angle A = 70°
- Angle B = 60°

2. **Find Angle C**:
- Use the angle sum property of a triangle, which states that the sum of the interior angles of a triangle is 180°.
- Therefore, we can write:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
- Substituting the known values:
\[ 70° + 60° + \text{Angle C} = 180° \]
- Simplifying:
\[ 130° + \text{Angle C} = 180° \]
- To find Angle C, subtract 130° from both sides:
\[ \text{Angle C} = 180° - 130° = 50° \]

3. **Calculate the Exterior Angles**:
- The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

- **Exterior Angle at A**:
- Opposite angles are B and C:
\[ \text{Exterior Angle A} = \text{Angle B} + \text{Angle C} = 60° + 50° = 110° \]

- **Exterior Angle at B**:
- Opposite angles are A and C:
\[ \text{Exterior Angle B} = \text{Angle A} + \text{Angle C} = 70° + 50° = 120° \]

- **Exterior Angle at C**:
- Opposite angles are A and B:
\[ \text{Exterior Angle C} = \text{Angle A} + \text{Angle B} = 70° + 60° = 130° \]

4. **Summary of Exterior Angles**:
- Exterior Angle A = 110°
- Exterior Angle B = 120°
- Exterior Angle C = 130°

### Conclusion:
The measures of the exterior angles of triangle ABC are:
- Exterior Angle A = 110°
- Exterior Angle B = 120°
- Exterior Angle C = 130°