If the sum of two angles is 135° and their difference is `pi`/12 , then the circular measure of the greater angle is.
यदि दो कोणों का योगफल 135° है और उनका अंतर `pi`/12 है, तो बड़े कोण का वृत्तीय माप है:

Options

A. A)`(2pi)/3`
B. B)`(3pi)/5`
C. C)`(5pi)/12`
D. D)`(pi)/3`

Explanation

To solve the problem, we need to find the circular measure of the greater angle given that the sum of two angles is 135° and their difference is π/12.

### Step-by-Step Solution:

1. **Set Up Equations**:
Let the two angles be \( A \) and \( B \).
We know:
\[ A + B = 135^\circ \quad \text{(1)} \]
\[ A - B = \frac{\pi}{12} \quad \text{(2)} \]

2. **Convert π/12 to Degrees**:
Since \( \pi \) radians is equivalent to \( 180^\circ \), we can convert \( \frac{\pi}{12} \) to degrees:
\[ \frac{\pi}{12} = \frac{180^\circ}{12} = 15^\circ \]
Thus, equation (2) becomes:
\[ A - B = 15^\circ \quad \text{(3)} \]

3. **Add Equations (1) and (3)**:
To find \( A \), we can add equations (1) and (3):
\[ (A + B) + (A - B) = 135^\circ + 15^\circ \]
This simplifies to:
\[ 2A = 150^\circ \]
Therefore:
\[ A = \frac{150^\circ}{2} = 75^\circ \]

4. **Substitute to Find B**:
Now we can substitute \( A \) back into equation (1) to find \( B \):
\[ 75^\circ + B = 135^\circ \]
Solving for \( B \):
\[ B = 135^\circ - 75^\circ = 60^\circ \]

5. **Identify the Greater Angle**:
The greater angle is \( A = 75^\circ \).

6. **Convert to Circular Measure**:
To find the circular measure of the greater angle, we convert \( 75^\circ \) to radians:
\[ \text{Circular Measure} = A \times \frac{\pi}{180^\circ} = 75^\circ \times \frac{\pi}{180^\circ} \]
Simplifying this:
\[ = \frac{75\pi}{180} = \frac{5\pi}{12} \]

### Final Answer:
The circular measure of the greater angle is \( \frac{5\pi}{12} \).

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