The number of diagonals of a polygon of 20 of sides

Options

A. 210
B. 190
C. 180
D. 170

Answer

To find the number of diagonals in a polygon with 20 sides, we can follow these steps:

### Step 1: Understand the formula for the number of diagonals
The formula to calculate the number of diagonals \( D \) in a polygon with \( n \) sides is given by:
\[ D = \frac{n(n-3)}{2} \]
where \( n \) is the number of sides of the polygon.

### Step 2: Substitute the value of \( n \)
In this case, the polygon has 20 sides, so we substitute \( n = 20 \) into the formula:
\[ D = \frac{20(20-3)}{2} \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ D = \frac{20 \times 17}{2} \]

### Step 4: Calculate the multiplication
Next, we calculate \( 20 \times 17 \):
\[ 20 \times 17 = 340 \]

### Step 5: Divide by 2
Now, we divide 340 by 2:
\[ D = \frac{340}{2} = 170 \]

### Conclusion
Thus, the number of diagonals in a polygon with 20 sides is:
\[ \boxed{170} \]