In a `/_\ ABC`, if `/_B = 40^(@)` and `/_C = 35^(@)`, then `/_A=?`

Options

A. `50^(@)`
B. `55^(@)`
C. `105^(@)`
D. `150^(@)`

Answer

To find the measure of angle A in triangle ABC, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Triangle Angle Sum Property**:
The sum of the angles in any triangle is always 180 degrees. This means:
\[ \angle A + \angle B + \angle C = 180^\circ \]

2. **Substitute the Known Angles**:
We are given that:
\[ \angle B = 40^\circ \quad \text{and} \quad \angle C = 35^\circ \]
Substitute these values into the equation:
\[ \angle A + 40^\circ + 35^\circ = 180^\circ \]

3. **Combine the Known Angles**:
Add the angles B and C:
\[ 40^\circ + 35^\circ = 75^\circ \]
So, the equation now becomes:
\[ \angle A + 75^\circ = 180^\circ \]

4. **Isolate Angle A**:
To find angle A, subtract 75 degrees from both sides:
\[ \angle A = 180^\circ - 75^\circ \]

5. **Calculate Angle A**:
Perform the subtraction:
\[ \angle A = 105^\circ \]

### Final Answer:
Thus, the measure of angle A is:
\[ \angle A = 105^\circ \]