In `DeltaABC` if `/_BAC=90^(@)` and `AB=AC`, then `/_ABC` is

Options

A. `30^(@)`
B. `60^(@)`
C. `45^(@)`
D. `25^(@)`

Answer

To solve the problem, we need to analyze the given information about triangle ABC:

1. **Given Information**:
- Angle BAC = 90 degrees (∠BAC = 90°)
- AB = AC (The sides opposite to angles ABC and ACB are equal)

2. **Understanding the Triangle**:
Since AB = AC, triangle ABC is an isosceles triangle with the right angle at A.

3. **Using the Triangle Sum Property**:
The sum of the angles in any triangle is 180 degrees. Therefore, we can write the equation:
\[ \angle ABC + \angle ACB + \angle BAC = 180° \]
Substituting the known values:
\[ \angle ABC + \angle ACB + 90° = 180° \]

4. **Simplifying the Equation**:
To find the sum of angles ABC and ACB, we can rearrange the equation:
\[ \angle ABC + \angle ACB = 180° - 90° = 90° \]

5. **Setting the Angles Equal**:
Since AB = AC, the angles opposite these sides (∠ABC and ∠ACB) must be equal. Let's denote these angles as x:
\[ \angle ABC = x \quad \text{and} \quad \angle ACB = x \]
Therefore, we can write:
\[ x + x = 90° \]
This simplifies to:
\[ 2x = 90° \]

6. **Solving for x**:
Dividing both sides by 2 gives:
\[ x = \frac{90°}{2} = 45° \]

7. **Conclusion**:
Thus, the measure of angle ABC (∠ABC) is 45 degrees.

### Final Answer:
\[ \angle ABC = 45° \]