Statement-1: A convex quindecagon has 90 diagonals.
Statement-2: Number of diagonals in a polygon is `.^(n)C_(2)-n`.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Explanation

To solve the problem, we need to verify both statements regarding the number of diagonals in a convex polygon, specifically a quindecagon (which has 15 sides).

### Step-by-Step Solution:

1. **Understanding the Statements**:
- **Statement 1**: A convex quindecagon has 90 diagonals.
- **Statement 2**: The formula for the number of diagonals in a polygon is given by \( \binom{n}{2} - n \), where \( n \) is the number of sides.

2. **Applying Statement 2**:
- First, we need to confirm Statement 2 by using the formula for the number of diagonals in a polygon.
- The formula for the number of diagonals \( D \) in a polygon with \( n \) sides is:
\[ D = \binom{n}{2} - n \]

3. **Calculating for a Quindecagon**:
- A quindecagon has \( n = 15 \) sides.
- We calculate \( \binom{15}{2} \):
\[ \binom{15}{2} = \frac{15 \times 14}{2} = \frac{210}{2} = 105 \]

4. **Finding the Number of Diagonals**:
- Now, we substitute \( \binom{15}{2} \) into the diagonal formula:
\[ D = 105 - 15 = 90 \]

5. **Conclusion**:
- We find that the number of diagonals in a convex quindecagon is indeed 90, confirming Statement 1.
- Since Statement 2 is also correct, we conclude that both statements are true.

### Final Answer:
Both Statement 1 and Statement 2 are true, and Statement 2 is a correct explanation for Statement 1.

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