If the angles of a triangle are in A.P., then the measures of one of the angles in radians is

Options

A. `pi/6`
B. `pi/3`
C. `pi/2`
D. `2pi/3`

Explanation

To solve the problem of finding the measures of one of the angles in a triangle when the angles are in Arithmetic Progression (A.P.), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Angles in A.P.**:
- Let the three angles of the triangle be represented as \( A - D \), \( A \), and \( A + D \), where \( A \) is the middle angle and \( D \) is the common difference.

2. **Using the Sum of Angles in a Triangle**:
- The sum of the angles in any triangle is \( \pi \) radians (or 180 degrees). Therefore, we can write the equation:
\[ (A - D) + A + (A + D) = \pi \]

3. **Simplifying the Equation**:
- When we simplify the left side, we get:
\[ A - D + A + A + D = 3A \]
- The \( -D \) and \( +D \) cancel each other out.

4. **Setting Up the Equation**:
- We now have:
\[ 3A = \pi \]

5. **Solving for A**:
- To find \( A \), we divide both sides of the equation by 3:
\[ A = \frac{\pi}{3} \]

6. **Conclusion**:
- Therefore, one of the angles in the triangle, which is \( A \), measures \( \frac{\pi}{3} \) radians.

### Final Answer:
The measure of one of the angles in radians is \( \frac{\pi}{3} \).

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