Triangle ABC has angle BAC equal to `90^(@).` What is the measure of the angle ABC? A. The angle ABC is `35^(@)` B. The angle CBA is `55^(@)`

Options

A. if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
B. if the statement B alone is sufficient to answer the question, the statement A alone is not sufficient.
C. if both statements A and B together are needed to answer the question.
D. if either the statement A alone or statement B alone is sufficient to answer the question

Explanation

To solve the problem, we need to find the measure of angle ABC in triangle ABC, where angle BAC is given as 90 degrees. We will analyze the two statements provided to see if either one or both are sufficient to determine the measure of angle ABC.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- We have triangle ABC with angle BAC = 90 degrees.
- By the triangle angle sum property, the sum of the angles in a triangle is always 180 degrees.

2. **Using the Triangle Angle Sum Property**:
- Let angle ABC = B and angle CBA = C.
- We know that:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
- Substituting the known angle:
\[ 90^\circ + B + C = 180^\circ \]
- This simplifies to:
\[ B + C = 90^\circ \quad \text{(Equation 1)} \]

3. **Analyzing Statement A**:
- Statement A states that angle ABC (B) = 35 degrees.
- Substituting this value into Equation 1:
\[ 35^\circ + C = 90^\circ \]
- Solving for C:
\[ C = 90^\circ - 35^\circ = 55^\circ \]
- Thus, statement A alone is sufficient to determine angle ABC (B = 35 degrees).

4. **Analyzing Statement B**:
- Statement B states that angle CBA (C) = 55 degrees.
- Substituting this value into Equation 1:
\[ B + 55^\circ = 90^\circ \]
- Solving for B:
\[ B = 90^\circ - 55^\circ = 35^\circ \]
- Thus, statement B alone is also sufficient to determine angle ABC (B = 35 degrees).

5. **Conclusion**:
- Since both statements A and B independently provide enough information to determine the measure of angle ABC, we conclude that either statement alone is sufficient.

### Final Answer:
The answer is that either statement A alone or statement B alone is sufficient to answer the question.