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 measure of one of the angles in a triangle where the angles are in Arithmetic Progression (A.P.), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles**:
Let the three angles of the triangle be represented as:
- First angle: \( A - D \)
- Second angle: \( A \)
- Third angle: \( A + D \)

2. **Use the Triangle Angle Sum Property**:
The sum of the angles in a triangle is always \( \pi \) radians. Therefore, we can set up the equation:
\[ (A - D) + A + (A + D) = \pi \]

3. **Simplify the Equation**:
Combine like terms:
\[ A - D + A + A + D = \pi \]
This simplifies to:
\[ 3A = \pi \]

4. **Solve for A**:
To find the value of \( A \), divide both sides of the equation by 3:
\[ A = \frac{\pi}{3} \]

5. **Identify the Angles**:
Now we can find the measures of the angles:
- First angle: \( A - D = \frac{\pi}{3} - D \)
- Second angle: \( A = \frac{\pi}{3} \)
- Third angle: \( A + D = \frac{\pi}{3} + D \)

6. **Conclusion**:
One of the angles in the triangle is \( \frac{\pi}{3} \) radians.

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

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