Find the number of diagonals of a 16-sided polygon.

Answer

To find the number of diagonals in a 16-sided polygon, we can use the formula for the number of diagonals in an n-sided polygon, which is given by:

\[ \text{Number of Diagonals} = \frac{n(n - 3)}{2} \]

**Step 1: Identify the number of sides (n) in the polygon.**
In this case, the polygon has 16 sides. Therefore, we have:

\[ n = 16 \]

**Step 2: Substitute the value of n into the formula.**
Now we substitute \( n = 16 \) into the formula:

\[ \text{Number of Diagonals} = \frac{16(16 - 3)}{2} \]

**Step 3: Simplify the expression inside the parentheses.**
Calculate \( 16 - 3 \):

\[ 16 - 3 = 13 \]

Now substitute this back into the formula:

\[ \text{Number of Diagonals} = \frac{16 \times 13}{2} \]

**Step 4: Calculate the product of 16 and 13.**
Now we calculate \( 16 \times 13 \):

\[ 16 \times 13 = 208 \]

**Step 5: Divide the result by 2.**
Now we divide 208 by 2:

\[ \frac{208}{2} = 104 \]

**Final Answer:**
The number of diagonals in a 16-sided polygon is \( 104 \).

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