If the exterior angle of a triangle is ` 130°` and its interior opposite angles are equal, then measure of each interior opposite angle is

Options

A. `55^@`
B. `65^@`
C. `50^@`
D. `60^@`

Answer

To solve the problem, we need to find the measure of each interior opposite angle of a triangle when given that the exterior angle is 130° and the interior opposite angles are equal. Here’s how to approach the problem step by step:

### Step-by-Step Solution:

1. **Understand the Triangle and Exterior Angle**:
- Let’s denote the triangle as ABC, where angle C is the vertex at which the exterior angle is formed.
- The exterior angle (angle ACX) is given as 130°.

2. **Identify the Interior Opposite Angles**:
- The interior opposite angles to the exterior angle ACX are angles A and B.
- According to the problem, angle A = angle B (let's denote both angles as x).

3. **Use the Exterior Angle Theorem**:
- The Exterior Angle Theorem states that the exterior angle is equal to the sum of the two opposite interior angles.
- Therefore, we can write the equation:
\[ \text{Angle ACX} = \text{Angle A} + \text{Angle B} \]
- Substituting the known values:
\[ 130° = x + x \]

4. **Simplify the Equation**:
- This simplifies to:
\[ 130° = 2x \]

5. **Solve for x**:
- To find the value of x, divide both sides of the equation by 2:
\[ x = \frac{130°}{2} = 65° \]

6. **Conclusion**:
- Therefore, the measure of each interior opposite angle (angle A and angle B) is 65°.

### Final Answer:
The measure of each interior opposite angle is **65°**.

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