The sum of the exterior angles of a convex n-sided polygon is half the sum of its interior angles. We are asked to find the number of sides, $n$.

1. Problem Description

The sum of the exterior angles of a convex n-sided polygon is half the sum of its interior angles. We are asked to find the number of sides, $n$.

2. Solution Steps

The sum of the exterior angles of any convex polygon is always $360^{\circ}$.

The sum of the interior angles of a convex n-sided polygon is given by the formula:

$(n-2) \times 180^{\circ}$.

The problem states that the sum of the exterior angles is half the sum of the interior angles. Therefore, we can write the equation:

$360 = \frac{1}{2} (n-2) \times 180$.

Multiplying both sides by 2, we have:

$720 = (n-2) \times 180$.

Dividing both sides by 180, we get:

$4 = n-2$.

Adding 2 to both sides, we find:

$n = 6$.

3. Final Answer

The number of sides of the polygon is

6. The answer is A. 6.