In `Delta ABC,`if BC=AB and `angleB=80^(@)`,then `angleA` is equal to

Options

A. `80^(@)`
B. `40^(@)`
C. `50^(@)`
D. `100^(@)`

Explanation

To solve the problem, we will use the properties of triangles. Here are the steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- In triangle ABC, we know that \( BC = AB \) (which means triangle ABC is isosceles with sides BC and AB being equal).
- We are also given that \( \angle B = 80^\circ \).

2. **Use the Property of Isosceles Triangles**:
- In an isosceles triangle, the angles opposite the equal sides are also equal. Since \( BC = AB \), it follows that \( \angle A = \angle C \).

3. **Set Up the Equation for Angles**:
- The sum of angles in any triangle is \( 180^\circ \). Therefore, we can write the equation:
\[ \angle A + \angle B + \angle C = 180^\circ \]
- Since \( \angle A = \angle C \), we can replace \( \angle C \) with \( \angle A \):
\[ \angle A + 80^\circ + \angle A = 180^\circ \]

4. **Combine Like Terms**:
- This simplifies to:
\[ 2\angle A + 80^\circ = 180^\circ \]

5. **Isolate \( \angle A \)**:
- Subtract \( 80^\circ \) from both sides:
\[ 2\angle A = 180^\circ - 80^\circ \]
\[ 2\angle A = 100^\circ \]

6. **Divide by 2**:
- Finally, divide both sides by 2 to find \( \angle A \):
\[ \angle A = \frac{100^\circ}{2} = 50^\circ \]

### Conclusion:
Thus, the measure of \( \angle A \) is \( 50^\circ \).