In right `triangle ABC `, `AB=BC` , then `angleA ` is equal to

Options

A. `45^(@)`
B. `90^(@)`
C. `60^(@)`
D. None of these

Answer

To solve the problem, we need to find the measure of angle A in right triangle ABC where AB = BC.

### Step-by-Step Solution:

1. **Identify the Triangle and Given Information**:
- We have a right triangle ABC.
- It is given that AB = BC.

2. **Determine the Hypotenuse**:
- In a right triangle, the hypotenuse is the longest side. Since AB and BC are equal, they cannot be the hypotenuse. Therefore, AC must be the hypotenuse.

3. **Identify the Right Angle**:
- In triangle ABC, angle B is the right angle (90 degrees).

4. **Apply the Property of Isosceles Triangles**:
- Since AB = BC, the angles opposite these sides must be equal. Therefore, angle A (opposite side BC) is equal to angle C (opposite side AB).

5. **Use the Angle Sum Property**:
- The sum of the angles in a triangle is 180 degrees. Thus, we can write:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
- Substituting the known values:
\[ \text{Angle A} + 90^\circ + \text{Angle A} = 180^\circ \]

6. **Simplify the Equation**:
- Combine like terms:
\[ 2 \cdot \text{Angle A} + 90^\circ = 180^\circ \]

7. **Isolate Angle A**:
- Subtract 90 degrees from both sides:
\[ 2 \cdot \text{Angle A} = 180^\circ - 90^\circ \]
\[ 2 \cdot \text{Angle A} = 90^\circ \]

8. **Solve for Angle A**:
- Divide both sides by 2:
\[ \text{Angle A} = \frac{90^\circ}{2} = 45^\circ \]

9. **Conclusion**:
- Therefore, the measure of angle A is 45 degrees.

### Final Answer:
Angle A is equal to 45 degrees.