Assertion (A) : If in a cyclic quadrilateral ,one angle is `40^(@)` ,then the opposite angle is `140^(@)` .
Reason (R ) : Sum of opposite angle in a cyclic quadrilateral is equal to `360^(@)`.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that in a cyclic quadrilateral, if one angle is \(40^\circ\), then the opposite angle is \(140^\circ\).
- Let's denote the angles of the cyclic quadrilateral as \(A\), \(B\), \(C\), and \(D\).
- According to the assertion, if \(A = 40^\circ\), we need to find the opposite angle \(C\).

2. **Using the Property of Cyclic Quadrilaterals**:
- A key property of cyclic quadrilaterals is that the sum of opposite angles is \(180^\circ\).
- This means that \(A + C = 180^\circ\) and \(B + D = 180^\circ\).

3. **Calculating the Opposite Angle**:
- Since we know \(A = 40^\circ\), we can substitute this into the equation:
\[ A + C = 180^\circ \]
\[ 40^\circ + C = 180^\circ \]
- To find \(C\), we subtract \(40^\circ\) from \(180^\circ\):
\[ C = 180^\circ - 40^\circ = 140^\circ \]

4. **Conclusion about Assertion (A)**:
- The assertion is true because we have shown that if one angle is \(40^\circ\), the opposite angle is indeed \(140^\circ\).

5. **Understanding the Reason (R)**:
- The reason states that the sum of opposite angles in a cyclic quadrilateral is equal to \(360^\circ\).
- This statement is incorrect. The correct property is that the sum of opposite angles in a cyclic quadrilateral is \(180^\circ\).

6. **Conclusion about Reason (R)**:
- Since the reason is false, we conclude that while the assertion is true, the reason is false.

### Final Conclusion:
- Assertion (A) is true.
- Reason (R) is false.