An n sided polygon has 'n' diagonals, then the value of n is :

Options

A. 4
B. 6
C. 7
D. 5

Answer

To find the value of \( n \) for an \( n \)-sided polygon that has \( n \) diagonals, we can follow these steps:

### Step 1: Understand the formula for the number of diagonals
The formula for the number of diagonals \( D \) in an \( n \)-sided polygon is given by:
\[ D = \frac{n(n-3)}{2} \]

### Step 2: Set up the equation
According to the problem, the number of diagonals is equal to \( n \). Therefore, we can set up the equation:
\[ \frac{n(n-3)}{2} = n \]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 2:
\[ n(n-3) = 2n \]

### Step 4: Rearrange the equation
Rearranging the equation gives:
\[ n^2 - 3n - 2n = 0 \]
This simplifies to:
\[ n^2 - 5n = 0 \]

### Step 5: Factor the equation
Factoring out \( n \) from the equation:
\[ n(n - 5) = 0 \]

### Step 6: Solve for \( n \)
Setting each factor to zero gives us:
1. \( n = 0 \)
2. \( n - 5 = 0 \) which gives \( n = 5 \)

Since \( n \) must be a positive integer representing the number of sides in a polygon, we discard \( n = 0 \).

### Final Answer
Thus, the value of \( n \) is:
\[ \boxed{5} \]

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