An exterior angle of a triangle is `125^(@)` and one of two interior opposite angle is `55^(@)`, then the other opposite interior angle is

Options

A. `70^(@)`
B. `55^(@)`
C. `60^(@)`
D. `80^(@)`

Answer

To solve the problem, we will use the property of exterior angles in a triangle. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

### Step-by-Step Solution:

1. **Identify the given values**:
- The exterior angle (∠ACD) is given as 125°.
- One of the opposite interior angles (∠ABC) is given as 55°.
- We need to find the other opposite interior angle (let's call it ∠BAC = x).

2. **Use the exterior angle property**:
According to the exterior angle property of triangles, we have:
\[ \text{Exterior Angle} = \text{Interior Angle 1} + \text{Interior Angle 2} \]
In our case:
\[ \angle ACD = \angle ABC + \angle BAC \]

3. **Substitute the known values into the equation**:
\[ 125° = 55° + x \]

4. **Solve for x**:
To find x, we rearrange the equation:
\[ x = 125° - 55° \]
\[ x = 70° \]

5. **Conclusion**:
The other opposite interior angle (∠BAC) is 70°.

### Final Answer:
The other opposite interior angle is **70°**.

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