In a triangle ABC, if `/_ A gt /_ B gt /_C` and the measures of `/_A , /_B ` and `/_ C` in degrees are integers, then the least possible value of `/_ A` is

Options

A. `70^(@)`
B. `65^(@)`
C. `60^(@)`
D. `61^(@)`

Explanation

To find the least possible value of angle A in triangle ABC, where angle A > angle B > angle C and all angles are integers, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles**:
Let angle C = X (the smallest angle), angle B = X + 1 (the middle angle), and angle A = X + 2 (the largest angle). This ensures that A > B > C.

2. **Set Up the Equation**:
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ A + B + C = 180 \]
Substituting the expressions for A, B, and C, we get:
\[ (X + 2) + (X + 1) + X = 180 \]

3. **Combine Like Terms**:
Simplifying the left side, we have:
\[ 3X + 3 = 180 \]

4. **Isolate X**:
To solve for X, subtract 3 from both sides:
\[ 3X = 180 - 3 \]
\[ 3X = 177 \]

5. **Divide by 3**:
Now, divide both sides by 3 to find X:
\[ X = \frac{177}{3} = 59 \]

6. **Calculate Angle A**:
Now that we have X, we can find angle A:
\[ A = X + 2 = 59 + 2 = 61 \]

7. **Conclusion**:
Therefore, the least possible value of angle A is:
\[ \boxed{61} \]