The number of diagonals in a 19 side polygon is:-
(a)152
(b)76
(c)114
(d)304

Options

A. 152
B. 76
C. 114
D. 304

Answer

To find the number of diagonals in a polygon with 19 sides, we can use the formula:

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

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

### Step-by-Step Solution:

1. **Identify the number of sides (N)**:
Here, \( N = 19 \).

2. **Substitute N into the formula**:
We substitute \( N \) into the formula:
\[ \text{Number of Diagonals} = \frac{19(19 - 3)}{2} \]

3. **Calculate \( N - 3 \)**:
Calculate \( 19 - 3 \):
\[ 19 - 3 = 16 \]

4. **Multiply N by \( N - 3 \)**:
Now, multiply \( 19 \) by \( 16 \):
\[ 19 \times 16 = 304 \]

5. **Divide by 2**:
Finally, divide \( 304 \) by \( 2 \):
\[ \frac{304}{2} = 152 \]

6. **Conclusion**:
Therefore, the number of diagonals in a 19-sided polygon is \( 152 \).

### Final Answer:
The answer is (a) 152.