Read the statements carefully and select the correct option.
Statement-1 : If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, then it is a rectangle.
Statement-II : If the sum of a pair of opposite angles of a quadrilateral is `180^@`, then the quadrilateral is cyclic.

Options

A. Both Statement-I and Statement-II are true.
B. Both Statement-I and Statement-II are false.
C. Statement-I is true but Statement-II is false.
D. Statement-I is false but Statement-II is true.

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** If the diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, then it is a rectangle.

- A cyclic quadrilateral is one where all vertices lie on a circle.
- If the diagonals are diameters of the circle, then they will intersect at the center of the circle.
- In a rectangle, opposite sides are equal and all angles are right angles (90 degrees).
- Since the diagonals are diameters, they will bisect each other at right angles, confirming that the angles formed are indeed 90 degrees.
- Therefore, this statement is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** If the sum of a pair of opposite angles of a quadrilateral is 180 degrees, then the quadrilateral is cyclic.

- A quadrilateral is cyclic if the sum of each pair of opposite angles is 180 degrees.
- This is a well-known property of cyclic quadrilaterals.
- Therefore, this statement is also **true**.

### Conclusion
Both statements are true. Therefore, the correct option is that both statements are true.

### Final Answer
Both Statement 1 and Statement 2 are true.