A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is
4
5
7
10
Step 1: Pick the two least consecutive primes.
They are \(2\) and \(3\).
Step 2: Add them to get the number of sides.
\(2 + 3 = 5\). So the polygon has \(n = 5\) sides (a pentagon).
Step 3: Use the diagonals formula.
Number of diagonals of an \(n\)-sided polygon:
\(\text{Diagonals} = \dfrac{n(n-3)}{2}\)
Step 4: Substitute \(n = 5\).
\(\text{Diagonals} = \dfrac{5(5-3)}{2}\)
Step 5: Simplify in small steps.
\(5-3 = 2\)
\(5 \times 2 = 10\)
\(\dfrac{10}{2} = 5\)
Conclusion: The polygon has \(5\) diagonals. Correct option: B (5).