How many diagonals are there in octagon?

Options

A. 12
B. 14
C. 20
D. 24

Answer

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

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

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution:

1. **Identify the number of sides in an octagon.**
- An octagon has 8 sides.
- Therefore, \( n = 8 \).

2. **Substitute the value of \( n \) into the formula.**
- We substitute \( n = 8 \) into the formula:
\[ \text{Number of diagonals} = \frac{8(8 - 3)}{2} \]

3. **Calculate \( n - 3 \).**
- Calculate \( 8 - 3 \):
\[ 8 - 3 = 5 \]

4. **Multiply \( n \) by \( n - 3 \).**
- Now, multiply \( 8 \) by \( 5 \):
\[ 8 \times 5 = 40 \]

5. **Divide the result by 2.**
- Finally, divide \( 40 \) by \( 2 \):
\[ \frac{40}{2} = 20 \]

6. **Conclusion.**
- Therefore, the number of diagonals in an octagon is \( 20 \).

### Final Answer:
The number of diagonals in an octagon is **20**.

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