Explanation:

- Let's denote the total number of enrolled voters as $x$.

- 10% did not vote, so 90% of $x$ cast their votes.

- The votes polled are $0.9x$.

- From these, 5% were invalid, so valid votes equal $95$ of the polled votes, which is $0.95\times 0.9x=0.855x$.

- The winning candidate got 55% of the valid votes. So they received $0.55\times 0.855x$.

- The opponent received $0.45\times 0.855x$.

- The difference between the winner and opponent was 1710 votes:

$$

(0.55 \times 0.855x) - (0.45 \times 0.855x) = 1710

$$

- This simplifies to:

$$

0.10 \times 0.855x = 1710

$$

- Solving for $x$:

$$

0.0855x = 1710 \implies x = \frac{1710}{0.0855} \approx 20000

$$

- So, the correct answer is Option 1: 20000.

.